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<section id="classes">
<h1>Classes<a class="headerlink" href="#classes" title="Permalink to this heading">#</a></h1>
<section id="module-toponetx.classes.cell_complex">
<span id="cell-complex"></span><h2>Cell Complex<a class="headerlink" href="#module-toponetx.classes.cell_complex" title="Permalink to this heading">#</a></h2>
<p>Creation and manipulation of a 2d cell complex.</p>
<p>The class also supports attaching arbitrary attributes and data to cells.</p>
<p>A cell complex is abbreviated in CX.</p>
<p>We reserve the notation CC for a combinatorial complex.</p>
<dl class="py class">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">toponetx.classes.cell_complex.</span></span><span class="sig-name descname"><span class="pre">CellComplex</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cells</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">regular</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">attr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex" title="Permalink to this definition">#</a></dt>
<dd><p>Class representing a cell complex.</p>
<p>A cell complex is a mathematical structure that is built up from simple building blocks called cells.
These cells can be thought of as generalized versions of familiar shapes, such as points, line segments,
triangles, and disks. By gluing these cells together in a prescribed way, one can create complex
geometrical objects that are of interest in topology and geometry.</p>
<p>Cell complexes can be used to represent various mathematical objects, such as graphs,
manifolds, and discrete geometric shapes. They are useful in many areas of mathematics,
such as algebraic topology and geometry, where they can be used to study the structure and
properties of these objects.</p>
<p>In TNX the class CellComplex supports building a regular or non-regular
2d cell complex. The class CellComplex only supports the construction
of 2d cell complexes. If higher dimensional cell complexes are desired
then one should utilize the class CombinatorialComplex.</p>
<p>Mathtmatically, in TNX a cell complex it a triplet (V, E, C)
where V is a set of nodes, E is a set of edges and C is a set of 2-cells.
In TNX each 2-cell C is consists of a finite sequence of nodes C=(n1,…,nk,n1) with k>=2.
All edges between two consecutive nodes in C belong to E.
Regular cells have unique nodes in C whereas non-regular cells allow for duplication.</p>
<p>In TNX cell complexes are implementes to be dynamic in the sense that
they can change by adding or subtracting objects (nodes, edges, 2-cells)
from them.</p>
<ol class="arabic simple">
<li><dl class="simple">
<dt>Dynamic construction of cell complexes, allowing users to add or remove objects from these</dt><dd><p>structures after their initial creation.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>Compatibility with the NetworkX library, enabling users to leverage the powerful algorithms</dt><dd><p>and data structures provided by this package.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>Support for attaching arbitrary attributes and data to cells in the complex, allowing users to store</dt><dd><p>and manipulate additional information about these objects.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>Efficient storage and manipulation of complex data structures, using advanced data structures</dt><dd><p>such as sparse matrices.</p>
</dd>
</dl>
</li>
<li><p>Robust error handling and validation of input data, ensuring that the package is reliable and easy to use.</p></li>
</ol>
<p class="rubric">Examples</p>
<p>Iteratively construct a cell complex:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="c1"># the cell [1, 2, 3, 4] consists of the cycle (1,2), (2,3), (3,4), (4,5)</span>
<span class="gp">>>> </span><span class="c1"># tnx creates these edges automatically if they are not inserted in the underlying graph</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
</pre></div>
</div>
<p>You can also pass a list of cells to the constructor:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">c1</span> <span class="o">=</span> <span class="n">Cell</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> <span class="c1"># a cell here is always assumed to be 2d</span>
<span class="gp">>>> </span><span class="n">c2</span> <span class="o">=</span> <span class="n">Cell</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="p">([</span><span class="n">c1</span><span class="p">,</span> <span class="n">c2</span><span class="p">])</span>
</pre></div>
</div>
<p>TopoNetX is also compatible with NetworkX, allowing users to create a cell complex from a NetworkX graph:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">networkx</span> <span class="k">as</span> <span class="nn">nx</span>
<span class="gp">>>> </span><span class="n">g</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">Graph</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">g</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">g</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">g</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cells_from</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">7</span><span class="p">]],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">cells</span>
</pre></div>
</div>
<p>By default, a regular cell complex is constructed. You can change this behaviour using the
<cite>regular</cite> parameter when constructing the complex.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="c1"># non-regular cell complex</span>
<span class="gp">>>> </span><span class="c1"># by default CellComplex constructor assumes regular cell complex</span>
<span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="p">(</span><span class="n">regular</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># non-regular 2-cell</span>
<span class="gp">>>> </span><span class="n">c1</span> <span class="o">=</span> <span class="n">Cell</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="n">regular</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">(</span><span class="n">c1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">is_regular</span>
</pre></div>
</div>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.add_cell">
<span class="sig-name descname"><span class="pre">add_cell</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cell</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rank</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">check_skeleton</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">attr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.add_cell"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.add_cell" title="Permalink to this definition">#</a></dt>
<dd><p>Add a single cell to cell complex.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>cell</strong> (<em>hashable or RankedEntity</em>) – If hashable the cell returned will be empty.</p></li>
<li><p><strong>rank</strong> (<em>int</em>) – rank of a cell, supported ranks is 1 or 2</p></li>
<li><p><strong>check_skeleton</strong> (<em>bool, default=False</em>) – If true, this function checks the skeleton whether the given cell can be added.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>Cell Complex</strong> (<em>CellComplex</em>)</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">c1</span> <span class="o">=</span> <span class="n">Cell</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'black'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">(</span><span class="n">c1</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'red'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'blue'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'green'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">cells</span><span class="p">[(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)][</span><span class="s1">'color'</span><span class="p">]</span>
<span class="go">'red'</span>
</pre></div>
</div>
<p class="rubric">Notes</p>
<ul class="simple">
<li><p>Rank must be 0,1,2</p></li>
</ul>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.add_cells_from">
<span class="sig-name descname"><span class="pre">add_cells_from</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cell_set</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rank</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">check_skeleton</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">attr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.add_cells_from"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.add_cells_from" title="Permalink to this definition">#</a></dt>
<dd><p>Add cells to cell complex.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>cell_set</strong> (<em>iterable of hashables or Cell</em>) – For hashables the cells returned will be empty.</p></li>
<li><p><strong>rank</strong> (<em>int (optional), default is None</em>) – when each element in cell_set is an iterable then
rank must be a number that indicates the rank
of the added cells.</p></li>
<li><p><strong>check_skeleton</strong> (<em>bool</em>) – If true, this function checks the skeleton whether the given cell can be added.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>Cell Complex</strong> (<em>CellComplex</em>)</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.add_edge">
<span class="sig-name descname"><span class="pre">add_edge</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">u_of_edge</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">v_of_edge</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">attr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.add_edge"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.add_edge" title="Permalink to this definition">#</a></dt>
<dd><p>Add edge.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.add_edges_from">
<span class="sig-name descname"><span class="pre">add_edges_from</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ebunch_to_add</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">attr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.add_edges_from"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.add_edges_from" title="Permalink to this definition">#</a></dt>
<dd><p>Add edges.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.add_node">
<span class="sig-name descname"><span class="pre">add_node</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">node</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">attr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.add_node"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.add_node" title="Permalink to this definition">#</a></dt>
<dd><p>Add a single node to cell complex.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.adjacency_matrix">
<span class="sig-name descname"><span class="pre">adjacency_matrix</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">rank</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">signed</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">index</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.adjacency_matrix"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.adjacency_matrix" title="Permalink to this definition">#</a></dt>
<dd><p>Compute adjacency matrix for a given rank.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.cell_diameter">
<span class="sig-name descname"><span class="pre">cell_diameter</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">s</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.cell_diameter"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.cell_diameter" title="Permalink to this definition">#</a></dt>
<dd><p>Return the length of the longest shortest s-walk between cells.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>s</strong> (<em>int, optional, default: 1</em>)</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>cell_diameter</strong> (<em>int</em>)</p>
</dd>
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>TopoNetXError</strong> – If cell complex is not s-cell-connected</p>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>Two cells are s-adjacent if they share s nodes.
Two nodes e_start and e_end are s-walk connected if there is a sequence of
cells e_start, e_1, e_2, … e_n-1, e_end such that consecutive cells
are s-adjacent. If the graph is not connected, an error will be raised.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.cell_diameters">
<span class="sig-name descname"><span class="pre">cell_diameters</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">s</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.cell_diameters"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.cell_diameters" title="Permalink to this definition">#</a></dt>
<dd><p>Return the cell diameters of the s_cell_connected component subgraphs.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>s</strong> (<em>int, optional, default: 1</em>)</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><ul class="simple">
<li><p><strong>maximum diameter</strong> (<em>int</em>)</p></li>
<li><p><strong>list of diameters</strong> (<em>list</em>) – List of cell_diameters for s-cell component subgraphs in CX</p></li>
<li><p><strong>list of component</strong> (<em>list</em>) – List of the cell uids in the s-cell component subgraphs.</p></li>
</ul>
</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.cell_distance">
<span class="sig-name descname"><span class="pre">cell_distance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">source</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">target</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">s</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.cell_distance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.cell_distance" title="Permalink to this definition">#</a></dt>
<dd><p>Return the shortest s-walk distance between two cells in the cell complex.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>source</strong> (<em>cell.uid or cell</em>) – a cell in the cell complex</p></li>
<li><p><strong>target</strong> (<em>cell.uid or cell</em>) – a cell in the cell complex</p></li>
<li><p><strong>s</strong> (<em>int</em>) – the number of intersections between pairwise consecutive cells</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>s- walk distance</strong> (<em>the shortest s-walk cell distance</em>) – A shortest s-walk is computed as a sequence of cells,
the s-walk distance is the number of cells in the sequence
minus 1. If no such path exists returns np.inf.</p>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#toponetx.classes.cell_complex.CellComplex.distance" title="toponetx.classes.cell_complex.CellComplex.distance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">distance</span></code></a></p>
</div>
<p class="rubric">Notes</p>
<p>The s-distance is the shortest s-walk length between the cells.
An s-walk between cells is a sequence of cells such that consecutive pairwise
cells intersect in at least s nodes. The length of the shortest s-walk is 1 less than
the number of cells in the path sequence.</p>
<p>Uses the networkx shortest_path_length method on the graph
generated by the s-cell_adjacency matrix.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.cell_neighbors">
<span class="sig-name descname"><span class="pre">cell_neighbors</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cell</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">s</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.cell_neighbors"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.cell_neighbors" title="Permalink to this definition">#</a></dt>
<dd><p>Cells in cell complex which share s nodes(s) with cells.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>cell</strong> (<em>hashable or RankedEntity</em>) – uid for a cell in cell complex or the cell RankedEntity</p></li>
<li><p><strong>s</strong> (<em>int, list, optional, default : 1</em>) – Minimum number of nodes shared by neighbors cell node.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><em>list</em> – List of cell neighbors.</p>
</dd>
</dl>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.cells">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">cells</span></span><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.cells" title="Permalink to this definition">#</a></dt>
<dd><p>Return cells.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.clear">
<span class="sig-name descname"><span class="pre">clear</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.clear"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.clear" title="Permalink to this definition">#</a></dt>
<dd><p>Remove all cells from a cell complex.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>cell complex</strong> (<em>CellComplex</em>)</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.coadjacency_matrix">
<span class="sig-name descname"><span class="pre">coadjacency_matrix</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">rank</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">signed</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">index</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.coadjacency_matrix"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.coadjacency_matrix" title="Permalink to this definition">#</a></dt>
<dd><p>Compute coadjacency matrix for a given rank.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.component_subgraphs">
<span class="sig-name descname"><span class="pre">component_subgraphs</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">return_singletons</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.component_subgraphs"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.component_subgraphs" title="Permalink to this definition">#</a></dt>
<dd><p>Compute s-component subgraphs with s=1.</p>
<p>Same as <code class="xref py py-meth docutils literal notranslate"><span class="pre">s_components_subgraphs()</span></code> with s=1. Returns iterator.</p>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#toponetx.classes.cell_complex.CellComplex.s_component_subgraphs" title="toponetx.classes.cell_complex.CellComplex.s_component_subgraphs"><code class="xref py py-obj docutils literal notranslate"><span class="pre">s_component_subgraphs</span></code></a></p>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.components">
<span class="sig-name descname"><span class="pre">components</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cells</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">return_singletons</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.components"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.components" title="Permalink to this definition">#</a></dt>
<dd><p>Compute s-component with s=1.</p>
<p>Same as <a class="reference internal" href="#toponetx.classes.cell_complex.CellComplex.s_connected_components" title="toponetx.classes.cell_complex.CellComplex.s_connected_components"><code class="xref py py-meth docutils literal notranslate"><span class="pre">s_connected_components()</span></code></a> with s=1.</p>
<p>But nodes are returned by default. Return iterator.</p>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#toponetx.classes.cell_complex.CellComplex.s_connected_components" title="toponetx.classes.cell_complex.CellComplex.s_connected_components"><code class="xref py py-obj docutils literal notranslate"><span class="pre">s_connected_components</span></code></a></p>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.connected_component_subgraphs">
<span class="sig-name descname"><span class="pre">connected_component_subgraphs</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">return_singletons</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.connected_component_subgraphs"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.connected_component_subgraphs" title="Permalink to this definition">#</a></dt>
<dd><p>Compute connected component subgraphs with s=1.</p>
<p>Same as <a class="reference internal" href="#toponetx.classes.cell_complex.CellComplex.s_component_subgraphs" title="toponetx.classes.cell_complex.CellComplex.s_component_subgraphs"><code class="xref py py-meth docutils literal notranslate"><span class="pre">s_component_subgraphs()</span></code></a> with s=1. Returns iterator.</p>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#toponetx.classes.cell_complex.CellComplex.s_component_subgraphs" title="toponetx.classes.cell_complex.CellComplex.s_component_subgraphs"><code class="xref py py-obj docutils literal notranslate"><span class="pre">s_component_subgraphs</span></code></a></p>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.connected_components">
<span class="sig-name descname"><span class="pre">connected_components</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cells</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">return_singletons</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.connected_components"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.connected_components" title="Permalink to this definition">#</a></dt>
<dd><p>Compute s-connected components with s=1.</p>
<p>Same as s_connected_component` with s=1, but nodes returned.</p>
<p>Return iterator.</p>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#toponetx.classes.cell_complex.CellComplex.s_connected_components" title="toponetx.classes.cell_complex.CellComplex.s_connected_components"><code class="xref py py-obj docutils literal notranslate"><span class="pre">s_connected_components</span></code></a></p>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.degree">
<span class="sig-name descname"><span class="pre">degree</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">node</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rank</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.degree"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.degree" title="Permalink to this definition">#</a></dt>
<dd><p>Compute the number of cells of certain rank that contain node.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>node</strong> (<em>hashable</em>) – Identifier for the node.</p></li>
<li><p><strong>rank</strong> (<em>positive integer, optional, default: 1</em>) – Smallest size of cell to consider in degree.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><em>int</em> – Number of cells of rank at least rank that contain node.</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.diameter">
<span class="sig-name descname"><span class="pre">diameter</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.diameter"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.diameter" title="Permalink to this definition">#</a></dt>
<dd><p>Return length of the longest shortest s-walk between nodes.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>s</strong> (<em>int, optional, default: 1</em>)</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>diameter</strong> (<em>int</em>)</p>
</dd>
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>TopoNetXError</strong> – If cx is not s-cell-connected</p>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>Two nodes are s-adjacent if they share s cells.
Two nodes v_start and v_end are s-walk connected if there is a sequence of
nodes v_start, v_1, v_2, … v_n-1, v_end such that consecutive nodes
are s-adjacent. If the graph is not connected, an error will be raised.</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.dim">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">dim</span></span><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.dim" title="Permalink to this definition">#</a></dt>
<dd><p>Return dimension.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.distance">
<span class="sig-name descname"><span class="pre">distance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">source</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">target</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">s</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.distance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.distance" title="Permalink to this definition">#</a></dt>
<dd><p>Return shortest s-walk distance between two nodes in the cell complex.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>source</strong> (<em>node.uid or node</em>) – a node in the CX</p></li>
<li><p><strong>target</strong> (<em>node.uid or node</em>) – a node in the CX</p></li>
<li><p><strong>s</strong> (<em>int</em>) – the number of cells</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>s-walk distance</strong> (<em>int</em>)</p>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#toponetx.classes.cell_complex.CellComplex.cell_distance" title="toponetx.classes.cell_complex.CellComplex.cell_distance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">cell_distance</span></code></a></p>
</div>
<p class="rubric">Notes</p>
<p>The s-distance is the shortest s-walk length between the nodes.
An s-walk between nodes is a sequence of nodes that pairwise share
at least s cells. The length of the shortest s-walk is 1 less than
the number of nodes in the path sequence.</p>
<p>Uses the networkx shortest_path_length method on the graph
generated by the s-adjacency matrix.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.down_laplacian_matrix">
<span class="sig-name descname"><span class="pre">down_laplacian_matrix</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">rank</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">signed</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weight</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">index</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.down_laplacian_matrix"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.down_laplacian_matrix" title="Permalink to this definition">#</a></dt>
<dd><p>Compute down laplacian.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>d</strong> (<em>int, dimension of the down Laplacian matrix.</em>) – Supported dimension are 0,1</p></li>
<li><p><strong>signed</strong> (<em>bool, is true return absolute value entry of the Laplacian matrix</em>) – this is useful when one needs to obtain higher-order
adjacency matrices from the hodge-laplacian
typically higher-order adjacency matrices’ entries are
typically positive.</p></li>
<li><p><strong>weight</strong> (<em>bool, default=False</em>) – If False all nonzero entries are 1.
If True and self.static all nonzero entries are filled by
self.cells.cell_weight dictionary values.</p></li>
<li><p><strong>index</strong> (<em>boolean, optional, default False</em>) – list identifying rows with nodes,edges or cells used to index the hodge Laplacian matrix
dependeing on the input dimension</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><ul class="simple">
<li><p><strong>down Laplacian</strong> (<em>scipy.sparse.csr.csr_matrix</em>)</p></li>
<li><p><em>when index is true</em> – return also a list : list
list identifying rows with nodes,edges or cells used to index the hodge Laplacian matrix
dependeing on the input dimension</p></li>
</ul>
</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">networkx</span> <span class="k">as</span> <span class="nn">nx</span>
<span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">path_graph</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">,)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">8</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">down_laplacian_matrix</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.edges">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">edges</span></span><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.edges" title="Permalink to this definition">#</a></dt>
<dd><p>Return edges.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.from_networkx_graph">
<span class="sig-name descname"><span class="pre">from_networkx_graph</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">G</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.from_networkx_graph"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.from_networkx_graph" title="Permalink to this definition">#</a></dt>
<dd><p>Add edges and nodes from a graph G to self.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cells_from</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">],[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">7</span><span class="p">]</span> <span class="p">],</span><span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">Graph</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">G</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">from_networkx_graph</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">edges</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.from_trimesh">
<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_trimesh</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mesh</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.from_trimesh"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.from_trimesh" title="Permalink to this definition">#</a></dt>
<dd><p>Convert from trimesh object.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">trimesh</span>
<span class="gp">>>> </span><span class="n">mesh</span> <span class="o">=</span> <span class="n">trimesh</span><span class="o">.</span><span class="n">Trimesh</span><span class="p">(</span><span class="n">vertices</span><span class="o">=</span><span class="p">[[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]],</span>
<span class="go"> faces=[[0, 1, 2]],</span>
<span class="go"> process=False)</span>
<span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="o">.</span><span class="n">from_trimesh</span><span class="p">(</span><span class="n">mesh</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">CX</span><span class="o">.</span><span class="n">nodes</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">CX</span><span class="o">.</span><span class="n">cells</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="s1">'position'</span><span class="p">]</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.get_cell_attributes">
<span class="sig-name descname"><span class="pre">get_cell_attributes</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">name</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rank</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.get_cell_attributes"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.get_cell_attributes" title="Permalink to this definition">#</a></dt>
<dd><p>Get node attributes from graph.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>name</strong> (<em>str</em>) – Attribute name</p></li>
<li><p><strong>rank</strong> (<em>int</em>) – rank of the k-cell</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><em>Dictionary of attributes keyed by cell or k-cells if k is not None</em></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">networkx</span> <span class="k">as</span> <span class="nn">nx</span>
<span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">path_graph</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">d</span> <span class="o">=</span> <span class="p">{((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="mi">0</span><span class="p">):</span> <span class="p">{</span><span class="s1">'color'</span><span class="p">:</span> <span class="s1">'red'</span><span class="p">,</span> <span class="s1">'attr2'</span><span class="p">:</span> <span class="mi">1</span><span class="p">},</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">):</span> <span class="p">{</span><span class="s1">'color'</span><span class="p">:</span> <span class="s1">'blue'</span><span class="p">,</span> <span class="s1">'attr2'</span><span class="p">:</span> <span class="mi">3</span> <span class="p">}}</span>
<span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">,)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">8</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">set_cell_attributes</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">get_cell_attributes</span><span class="p">(</span><span class="s1">'color'</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="go">{((1, 2, 3, 4), 0): 'red', (1, 2, 4): 'blue'}</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.get_filtration">
<span class="sig-name descname"><span class="pre">get_filtration</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">name</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.get_filtration"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.get_filtration" title="Permalink to this definition">#</a></dt>
<dd><p>Get filtration.</p>
<p class="rubric">Notes</p>
<p>This is equivalent to getting a feature defined on the entire cell complex</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">path_graph</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">d</span> <span class="o">=</span> <span class="p">{</span><span class="mi">0</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">):</span> <span class="mi">3</span><span class="p">}</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">set_filtration</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="s2">"f"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">get_filtration</span><span class="p">(</span><span class="s2">"f"</span><span class="p">)</span>
<span class="go">{0: 1, 1: 0, 2: 2, (0, 1): 1, (1, 2): 3}</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.hodge_laplacian_matrix">
<span class="sig-name descname"><span class="pre">hodge_laplacian_matrix</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">rank</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">signed</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weight</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">index</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.hodge_laplacian_matrix"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.hodge_laplacian_matrix" title="Permalink to this definition">#</a></dt>
<dd><p>Compute the hodge-laplacian matrix for the CX.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>rank</strong> (<em>int, dimension of the Laplacian matrix.</em>) – Supported dimension are 0, 1 and 2</p></li>
<li><p><strong>signed</strong> (<em>bool, is true return absolute value entry of the Laplacian matrix</em>) – this is useful when one needs to obtain higher-order
adjacency matrices from the hodge-laplacian
typically higher-order adjacency matrices’ entries are
typically positive.</p></li>
<li><p><strong>weight</strong> (<em>bool, default=False</em>) – If False all nonzero entries are 1.
If True and self.static all nonzero entries are filled by
self.cells.cell_weight dictionary values.</p></li>
<li><p><strong>index</strong> (<em>boolean, optional, default False</em>) – indicates wheather to return the indices that define the incidence matrix</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><ul class="simple">
<li><p><strong>Laplacian</strong> (<em>scipy.sparse.csr.csr_matrix</em>)</p></li>
<li><p><em>when index is true</em> – return also a list : list
list identifying rows with nodes,edges or cells used to index the hodge Laplacian matrix
depending on the input dimension</p></li>
</ul>
</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">hodge_laplacian_matrix</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.incidence_matrix">
<span class="sig-name descname"><span class="pre">incidence_matrix</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">rank</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">signed</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weight</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">index</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.incidence_matrix"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.incidence_matrix" title="Permalink to this definition">#</a></dt>
<dd><p>Incidence matrix for the cx indexed by nodes x cells.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>rank</strong> (<em>int</em>) – The rank for which an incidence matrix should be computed.</p></li>
<li><p><strong>signed</strong> (<em>bool, default=True</em>) – Whether the returned incidence matrix should be signed (i.e., respect orientations) or unsigned.</p></li>
<li><p><strong>weight</strong> (<em>bool, default=False</em>) – If False all nonzero entries are 1.
If True and self.static all nonzero entries are filled by
self.cells.cell_weight dictionary values.</p></li>
<li><p><strong>index</strong> (<em>boolean, optional, default False</em>) – If True return will include a dictionary of node uid : row number
and cell uid : column number</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><ul class="simple">
<li><p><strong>incidence_matrix</strong> (<em>scipy.sparse.csr.csr_matrix</em>)</p></li>
<li><p><strong>row list</strong> (<em>list</em>) – list of cells in the complex with the same
order of the row of the matrix</p></li>
<li><p><strong>column list</strong> (<em>list</em>) – list of cells in the complex with the same
order of the column of the matrix</p></li>
</ul>
</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">B0</span> <span class="o">=</span> <span class="n">CX</span><span class="o">.</span><span class="n">incidence_matrix</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">B1</span> <span class="o">=</span> <span class="n">CX</span><span class="o">.</span><span class="n">incidence_matrix</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">B2</span> <span class="o">=</span> <span class="n">CX</span><span class="o">.</span><span class="n">incidence_matrix</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">B1</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">B2</span><span class="p">)</span><span class="o">.</span><span class="n">todense</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">B0</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">B1</span><span class="p">)</span><span class="o">.</span><span class="n">todense</span><span class="p">()</span>
</pre></div>
</div>
<p>Note that in this example, the first three cells are equivalent and hence they have similar incidence to lower
edges they are incident to.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">networkx</span> <span class="k">as</span> <span class="nn">nx</span>
<span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">path_graph</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">4</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">,)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">8</span><span class="p">],</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">B1</span> <span class="o">=</span> <span class="n">CX</span><span class="o">.</span><span class="n">incidence_matrix</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">B2</span> <span class="o">=</span> <span class="n">CX</span><span class="o">.</span><span class="n">incidence_matrix</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">B1</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">B2</span><span class="p">)</span><span class="o">.</span><span class="n">todense</span><span class="p">()</span>
</pre></div>
</div>
<p>Non-regular cell complex example:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="p">(</span><span class="n">regular</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">],</span><span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">],</span><span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">B1</span> <span class="o">=</span> <span class="n">CX</span><span class="o">.</span><span class="n">incidence_matrix</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">B2</span> <span class="o">=</span> <span class="n">CX</span><span class="o">.</span><span class="n">incidence_matrix</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">B2</span><span class="o">.</span><span class="n">todense</span><span class="p">())</span> <span class="c1"># observe the non-unit entries</span>
<span class="gp">>>> </span><span class="n">B1</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">B2</span><span class="p">)</span><span class="o">.</span><span class="n">todense</span><span class="p">()</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">CX</span> <span class="o">=</span> <span class="n">CellComplex</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span><span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">CX</span><span class="o">.</span><span class="n">add_cell</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">],</span><span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">row</span><span class="p">,</span><span class="n">column</span><span class="p">,</span><span class="n">B1</span> <span class="o">=</span> <span class="n">CX</span><span class="o">.</span><span class="n">incidence_matrix</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">index</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">row</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">column</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">B1</span><span class="o">.</span><span class="n">todense</span><span class="p">())</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="toponetx.classes.cell_complex.CellComplex.is_connected">
<span class="sig-name descname"><span class="pre">is_connected</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">s</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cells</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/toponetx/classes/cell_complex.html#CellComplex.is_connected"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#toponetx.classes.cell_complex.CellComplex.is_connected" title="Permalink to this definition">#</a></dt>
<dd><p>Determine if cell complex is s-connected.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>s</strong> (<em>int, optional, default: 1</em>)</p></li>
<li><p><strong>cells</strong> (<em>boolean, optional, default: False</em>) – If True, will determine if s-cell-connected.
For s=1 s-cell-connected is the same as s-connected.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>