cdlib.evaluation.expansion

cdlib.evaluation.expansion(graph: Graph, community: object, summary: bool = True) → object

Number of edges per community node that point outside the cluster.

\[f(S) = \frac{c_S}{n_S}\]

where \(c_S\) is the number of edges on the community boundary, \(n_S\) is the number of community nodes.

Parameters:

  • graph – a networkx/igraph object

  • community – NodeClustering object

  • summary – boolean. If True it is returned an aggregated score for the partition is returned, otherwise individual-community ones. Default True.

Returns:

If summary==True a FitnessResult object, otherwise a list of floats.

Example:

>>> from cdlib.algorithms import louvain
>>> from cdlib import evaluation
>>> g = nx.karate_club_graph()
>>> communities = louvain(g)
>>> mod = evaluation.expansion(g,communities)
References:

  1. Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., & Parisi, D. (2004). Defining and identifying communities in networks. Proceedings of the National Academy of Sciences, 101(9), 2658-2663.