Merge pull request #1815 from Overriders/ring-of-cliques

Add generator for a ring of cliques graph

doc/source/reference/generators.rst

@@ -218,6 +218,7 @@ Community
    random_partition_graph
    planted_partition_graph
    gaussian_random_partition_graph
+   ring_of_cliques
 
 
 Non Isomorphic Trees

networkx/generators/community.py

@@ -3,16 +3,20 @@
 import math
 import random
 import networkx as nx
-#    Copyright(C) 2011 by
+#    Copyright(C) 2011, 2015 by
 #    Ben Edwards <bedwards@cs.unm.edu>
 #    Aric Hagberg <hagberg@lanl.gov>
+#    Konstantinos Karakatsanis <dinoskarakas@gmail.com>
 #    All rights reserved.
 #    BSD license.
 __author__ = """\n""".join(['Ben Edwards (bedwards@cs.unm.edu)',
-                            'Aric Hagberg (hagberg@lanl.gov)'])
+                            'Aric Hagberg (hagberg@lanl.gov)',
+                            'Konstantinos Karakatsanis '
+                            '<dinoskarakas@gmail.com>'])
 __all__ = ['caveman_graph', 'connected_caveman_graph',
            'relaxed_caveman_graph', 'random_partition_graph',
-           'planted_partition_graph', 'gaussian_random_partition_graph']
+           'planted_partition_graph', 'gaussian_random_partition_graph',
+           'ring_of_cliques']
 
 
 def caveman_graph(l, k):
@@ -406,3 +410,57 @@ def gaussian_random_partition_graph(n, s, v, p_in, p_out, directed=False,
         assigned += size
         sizes.append(size)
     return random_partition_graph(sizes, p_in, p_out, directed, seed)
+
+
+def ring_of_cliques(num_cliques, clique_size):
+    """Defines a "ring of cliques" graph.
+
+    A ring of cliques graph is consisting of cliques, connected through single
+    links. Each clique is a complete graph.
+
+    Parameters
+    ----------
+    num_cliques : int
+      Number of cliques
+    clique_size : int
+      Size of cliques
+
+    Returns
+    -------
+    G : NetworkX Graph
+      ring of cliques graph
+
+    Raises
+    ------
+    NetworkXError
+        If the number of cliques is lower than 2 or
+        if the size of cliques is smaller than 2.
+
+    Examples
+    --------
+    >>> G = nx.ring_of_cliques(8, 4)
+
+    See Also
+    --------
+    connected_caveman_graph
+
+    Notes
+    -----
+    The `connected_caveman_graph` graph removes a link from each clique to
+    connect it with the next clique. Instead, the `ring_of_cliques` graph
+    simply adds the link without removing any link from the cliques.
+    """
+    if num_cliques < 2:
+        raise nx.NetworkXError('A ring of cliques must have at least '
+                               'two cliques')
+    if clique_size < 2:
+        raise nx.NetworkXError('The cliques must have at least two nodes')
+
+    G = nx.Graph()
+    for i in range(num_cliques):
+        edges = itertools.combinations(range(i*clique_size, i*clique_size +
+                                             clique_size), 2)
+        G.add_edges_from(edges)
+        G.add_edge(i*clique_size+1, (i+1)*clique_size %
+                   (num_cliques*clique_size))
+    return G

networkx/generators/tests/test_community.py

@@ -110,3 +110,16 @@ def test_gaussian_random_partition_graph():
     assert_raises(nx.NetworkXError,
                   nx.gaussian_random_partition_graph, 100, 101, 10, 1, 0)
 
+def test_ring_of_cliques():
+    for i in range(2, 20):
+            for j in range(2, 20):
+                G = nx.ring_of_cliques(i, j)
+                assert_equal(G.number_of_nodes(), i*j)
+                if i != 2 or j != 1:
+                    expected_num_edges = i * (((j * (j - 1)) // 2) + 1)
+                else:
+                    # the edge that already exists cannot be duplicated
+                    expected_num_edges = i * (((j * (j - 1)) // 2) + 1) - 1
+                assert_equal(G.number_of_edges(), expected_num_edges)
+    assert_raises(nx.NetworkXError, nx.ring_of_cliques, 1, 5)
+    assert_raises(nx.NetworkXError, nx.ring_of_cliques, 3, 0)