# greedy_modularity_communities#

greedy_modularity_communities(G, weight=None, resolution=1, cutoff=1, best_n=None, n_communities=None)[source]#

Find communities in G using greedy modularity maximization.

This function uses Clauset-Newman-Moore greedy modularity maximization [2] to find the community partition with the largest modularity.

Greedy modularity maximization begins with each node in its own community and repeatedly joins the pair of communities that lead to the largest modularity until no futher increase in modularity is possible (a maximum). Two keyword arguments adjust the stopping condition. cutoff is a lower limit on the number of communities so you can stop the process before reaching a maximum (used to save computation time). best_n is an upper limit on the number of communities so you can make the process continue until at most n communities remain even if the maximum modularity occurs for more. To obtain exactly n communities, set both cutoff and best_n to n.

This function maximizes the generalized modularity, where resolution is the resolution parameter, often expressed as $$\gamma$$. See modularity().

Parameters
GNetworkX graph
weightstring or None, optional (default=None)

The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node.

resolutionfloat, optional (default=1)

If resolution is less than 1, modularity favors larger communities. Greater than 1 favors smaller communities.

cutoffint, optional (default=1)

A minimum number of communities below which the merging process stops. The process stops at this number of communities even if modularity is not maximized. The goal is to let the user stop the process early. The process stops before the cutoff if it finds a maximum of modularity.

best_nint or None, optional (default=None)

A maximum number of communities above which the merging process will not stop. This forces community merging to continue after modularity starts to decrease until best_n communities remain. If None, don’t force it to continue beyond a maximum.

n_communitiesint or None, optional (default=None)

Deprecated since version 3.0: The n_communities parameter is deprecated - use cutoff and/or best_n to set bounds on the desired number of communities instead.

A minimum number of communities below which the merging process stops. The process stops at this number of communities even if modularity is not maximized. The goal is to let the user stop the process early. The process stops before the cutoff if it finds a maximum of modularity.

Returns
communities: list

A list of frozensets of nodes, one for each community. Sorted by length with largest communities first.

Raises
ValueErrorIf the cutoff or best_n value is not in the range

[1, G.number_of_nodes()], or if best_n < cutoff. Also raised if cutoff is used with the deprecated n_communities parameter.

modularity

References

1

Newman, M. E. J. “Networks: An Introduction”, page 224 Oxford University Press 2011.

2

Clauset, A., Newman, M. E., & Moore, C. “Finding community structure in very large networks.” Physical Review E 70(6), 2004.

3

Reichardt and Bornholdt “Statistical Mechanics of Community Detection” Phys. Rev. E74, 2006.

4

Newman, M. E. J.”Analysis of weighted networks” Physical Review E 70(5 Pt 2):056131, 2004.

Examples

>>> from networkx.algorithms.community import greedy_modularity_communities
>>> G = nx.karate_club_graph()
>>> c = greedy_modularity_communities(G)
>>> sorted(c[0])
[8, 14, 15, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33]