Merge c24f37b into 8ce5bde

pygsp/graphs/__init__.py

@@ -137,6 +137,16 @@
 
 .. _NetworkX's documentation: https://networkx.github.io/documentation/stable/reference/generators.html
 
+Graphs built from other graphs
+------------------------------
+
+.. autosummary::
+
+    LineGraph
+
+Generated graphs
+----------------
+
 .. autosummary::
 
     Airfoil
@@ -186,6 +196,7 @@
     'ErdosRenyi',
     'FullConnected',
     'Grid2d',
+    'LineGraph',
     'Logo',
     'LowStretchTree',
     'Minnesota',

pygsp/graphs/linegraph.py

@@ -0,0 +1,47 @@
+# -*- coding: utf-8 -*-
+
+import numpy as np
+from scipy import sparse
+
+from . import Graph  # prevent circular import in Python < 3.5
+
+
+class LineGraph(Graph):
+    r"""Build the line graph of a graph.
+
+    Each vertex of the line graph represents an edge in the original graph. Two
+    vertices are connected if the edges they represent share a vertex in the
+    original graph.
+
+    Parameters
+    ----------
+    graph : :class:`Graph`
+
+    Examples
+    --------
+    >>> import matplotlib.pyplot as plt
+    >>> graph = graphs.Sensor(5, k=2, seed=10)
+    >>> line_graph = graphs.LineGraph(graph)
+    >>> fig, ax = plt.subplots()
+    >>> fig, ax = graph.plot('blue', edge_color='blue', indices=True, ax=ax)
+    >>> fig, ax = line_graph.plot('red', edge_color='red', indices=True, ax=ax)
+    >>> _ = ax.set_title('graph and its line graph')
+
+    """
+
+    def __init__(self, graph, **kwargs):
+
+        graph.compute_differential_operator()
+        # incidence = np.abs(graph.D)  # weighted?
+        incidence = (graph.D != 0)
+
+        adjacency = incidence.T.dot(incidence).astype(np.int)
+        adjacency -= sparse.identity(graph.n_edges, dtype=np.int)
+
+        try:
+            coords = incidence.T.dot(graph.coords) / 2
+        except AttributeError:
+            coords = None
+
+        super(LineGraph, self).__init__(adjacency, coords=coords,
+                plotting=graph.plotting, **kwargs)

pygsp/tests/test_graphs.py

@@ -448,6 +448,38 @@ def test_set_coordinates(self):
         G.set_coordinates('community2D')
         self.assertRaises(ValueError, G.set_coordinates, 'invalid')
 
+    def test_line_graph(self):
+        adjacency = [
+            [0, 1, 1, 3],
+            [1, 0, 1, 0],
+            [1, 1, 0, 1],
+            [3, 0, 1, 0],
+        ]
+        coords = [
+            [0, 0],
+            [4, 0],
+            [4, 2],
+            [0, 2],
+        ]
+        graph = graphs.Graph(adjacency, coords=coords)
+        graph = graphs.LineGraph(graph)
+        adjacency = [
+            [0, 1, 1, 1, 0],
+            [1, 0, 1, 1, 1],
+            [1, 1, 0, 0, 1],
+            [1, 1, 0, 0, 1],
+            [0, 1, 1, 1, 0],
+        ]
+        coords = [
+            [2, 0],
+            [2, 1],
+            [0, 1],
+            [4, 1],
+            [2, 2],
+        ]
+        np.testing.assert_equal(graph.W.toarray(), adjacency)
+        np.testing.assert_equal(graph.coords, coords)
+
     def test_subgraph(self, n_vertices=100):
         self._G.set_signal(self._G.coords, 'coords')
         graph = self._G.subgraph(range(n_vertices))

pygsp/tests/test_plotting.py

@@ -54,6 +54,8 @@ def test_plot_graphs(self):
                 Gs.append(Graph(Xin))
             elif classname in ['ImgPatches', 'Grid2dImgPatches']:
                 Gs.append(Graph(img=self._img, patch_shape=(3, 3)))
+            elif classname == 'LineGraph':
+                Gs.append(Graph(graphs.Sensor(20, seed=42)))
             else:
                 Gs.append(Graph())