cdlib.evaluation.erdos_renyi_modularity

erdos_renyi_modularity(graph: <Mock id='140619399400656'>, communities: object, **kwargs) → object

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 \(p\).

\[Q(S) = \frac{1}{m}\sum_{c \in S} (m_S − \frac{mn_S(n_S −1)}{n(n−1)})\]

where \(m\) is the number of graph edges, \(m_S\) is the number of community edges, \(l_S\) is the number of edges from nodes in S to nodes outside S.

Parameters:
  • graph – a networkx/igraph object
  • communities – NodeClustering object
Returns:

FitnessResult object

Example:

>>> from cdlib.algorithms import louvain
>>> from cdlib import evaluation
>>> g = nx.karate_club_graph()
>>> communities = louvain(g)
>>> mod = evaluation.erdos_renyi_modularity(g,communities)
References:
  1. Erdos, P., & Renyi, A. (1959). On random graphs I. Publ. Math. Debrecen, 6, 290-297.