rber_pots(g_original: object, initial_membership: list = None, weights: list = None, node_sizes: list = None, resolution_parameter: float = 1) → cdlib.classes.node_clustering.NodeClustering

rber_pots is a model where the quality function to optimize is:

\[Q = \sum_{ij} \left(A_{ij} - \gamma p \right)\delta(\sigma_i, \sigma_j)\]

where \(A\) is the adjacency matrix, \(p = \frac{m}{\binom{n}{2}}\) is the overall density of the graph, \(\sigma_i\) denotes the community of node \(i\), \(\delta(\sigma_i, \sigma_j) = 1\) if \(\sigma_i = \sigma_j\) and 0 otherwise, and, finally \(\gamma\) is a resolution parameter.

Supported Graph Types

Undirected Directed Weighted
Yes No No
  • g_original – a networkx/igraph object
  • initial_membership – list of int Initial membership for the partition. If None then defaults to a singleton partition. Deafault None
  • weights – list of double, or edge attribute Weights of edges. Can be either an iterable or an edge attribute. Deafault None
  • node_sizes – list of int, or vertex attribute Sizes of nodes are necessary to know the size of communities in aggregate graphs. Usually this is set to 1 for all nodes, but in specific cases this could be changed. Deafault None
  • resolution_parameter – double >0 A parameter value controlling the coarseness of the clustering. Higher resolutions lead to more communities, while lower resolutions lead to fewer communities. Deafault 1

NodeClustering object

>>> from cdlib import algorithms
>>> import networkx as nx
>>> G = nx.karate_club_graph()
>>> coms = algorithms.rber_pots(G)

Reichardt, J., & Bornholdt, S. (2006). Statistical mechanics of community detection. Physical Review E, 74(1), 016110. 10.1103/PhysRevE.74.016110


Reference implementation: