def erdos_renyi_modularity(self):
"""
Erdos-Renyi modularity is a variation of the Newman-Girvan one.
It assumes that vertices in a network are connected randomly with a constant probability :math:`p`.
.. math:: Q(S) = \\frac{1}{m}\\sum_{c \\in S} (m_S − \\frac{mn_S(n_S −1)}{n(n−1)})
where :math:`m` is the number of graph edges, :math:`m_S` is the number of algorithms edges, :math:`l_S` is the number of edges from nodes in S to nodes outside S.
:return: the Erdos-Renyi modularity score
:Example:
>>> from cdlib.algorithms import louvain
>>> g = nx.karate_club_graph()
>>> communities = louvain(g)
>>> mod = communities.erdos_renyi_modularity()
:References:
Erdos, P., & Renyi, A. (1959). **On random graphs I.** Publ. Math. Debrecen, 6, 290-297.
"""
if self.__check_graph():
return evaluation.erdos_renyi_modularity(self.graph, self)
else:
raise ValueError("Graph instance not specified")
def test_modularity(self):
g = nx.karate_club_graph()
communities = louvain(g)
mod = evaluation.newman_girvan_modularity(g, communities)
self.assertLessEqual(mod.score, 1)
self.assertGreaterEqual(mod.score, -0.5)
mod = evaluation.erdos_renyi_modularity(g, communities)
self.assertLessEqual(mod.score, 1)
self.assertGreaterEqual(mod.score, -0.5)
mod = evaluation.modularity_density(g, communities)
self.assertIsInstance(mod.score, float)
mod = evaluation.z_modularity(g, communities)
self.assertLessEqual(mod.score, np.sqrt(g.number_of_nodes()))
self.assertGreaterEqual(mod.score, -0.5)
