community API

This package implements community detection.

Package name is community but refer to python-louvain on pypi

community.best_partition(graph, partition=None, weight='weight', resolution=1.0, randomize=None, random_state=None)

Compute the partition of the graph nodes which maximises the modularity (or try..) using the Louvain heuristices

This is the partition of highest modularity, i.e. the highest partition of the dendrogram generated by the Louvain algorithm.

Parameters
graphnetworkx.Graph

the networkx graph which is decomposed

partitiondict, optional

the algorithm will start using this partition of the nodes. It’s a dictionary where keys are their nodes and values the communities

weightstr, optional

the key in graph to use as weight. Default to ‘weight’

resolutiondouble, optional

Will change the size of the communities, default to 1. represents the time described in “Laplacian Dynamics and Multiscale Modular Structure in Networks”, R. Lambiotte, J.-C. Delvenne, M. Barahona

randomizeboolean, optional

Will randomize the node evaluation order and the community evaluation order to get different partitions at each call

random_stateint, RandomState instance or None, optional (default=None)

If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Returns
partitiondictionnary

The partition, with communities numbered from 0 to number of communities

Raises
NetworkXError

If the graph is not Eulerian.

See also

generate_dendrogram

to obtain all the decompositions levels

Notes

Uses Louvain algorithm

References

large networks. J. Stat. Mech 10008, 1-12(2008).

Examples

>>> # basic usage
>>> import community as community_louvain
>>> import networkx as nx
>>> G = nx.erdos_renyi_graph(100, 0.01)
>>> partion = community_louvain.best_partition(G)

>>> # display a graph with its communities:
>>> # as Erdos-Renyi graphs don't have true community structure,
>>> # instead load the karate club graph
>>> import community as community_louvain
>>> import matplotlib.cm as cm
>>> import matplotlib.pyplot as plt
>>> import networkx as nx
>>> G = nx.karate_club_graph()
>>> # compute the best partition
>>> partition = community_louvain.best_partition(G)

>>> # draw the graph
>>> pos = nx.spring_layout(G)
>>> # color the nodes according to their partition
>>> cmap = cm.get_cmap('viridis', max(partition.values()) + 1)
>>> nx.draw_networkx_nodes(G, pos, partition.keys(), node_size=40, 
>>>                        cmap=cmap, node_color=list(partition.values()))
>>> nx.draw_networkx_edges(G, pos, alpha=0.5)
>>> plt.show()
community.generate_dendrogram(graph, part_init=None, weight='weight', resolution=1.0, randomize=None, random_state=None)

Find communities in the graph and return the associated dendrogram

A dendrogram is a tree and each level is a partition of the graph nodes. Level 0 is the first partition, which contains the smallest communities, and the best is len(dendrogram) - 1. The higher the level is, the bigger are the communities

Parameters
graphnetworkx.Graph

the networkx graph which will be decomposed

part_initdict, optional

the algorithm will start using this partition of the nodes. It’s a dictionary where keys are their nodes and values the communities

weightstr, optional

the key in graph to use as weight. Default to ‘weight’

resolutiondouble, optional

Will change the size of the communities, default to 1. represents the time described in “Laplacian Dynamics and Multiscale Modular Structure in Networks”, R. Lambiotte, J.-C. Delvenne, M. Barahona

Returns
dendrogramlist of dictionaries

a list of partitions, ie dictionnaries where keys of the i+1 are the values of the i. and where keys of the first are the nodes of graph

Raises
TypeError

If the graph is not a networkx.Graph

See also

best_partition

Notes

Uses Louvain algorithm

References

networks. J. Stat. Mech 10008, 1-12(2008).

Examples

>>> G=nx.erdos_renyi_graph(100, 0.01)
>>> dendo = generate_dendrogram(G)
>>> for level in range(len(dendo) - 1) :
>>>     print("partition at level", level,
>>>           "is", partition_at_level(dendo, level))
:param weight:
:type weight:
community.induced_graph(partition, graph, weight='weight')

Produce the graph where nodes are the communities

there is a link of weight w between communities if the sum of the weights of the links between their elements is w

Parameters
partitiondict

a dictionary where keys are graph nodes and values the part the node belongs to

graphnetworkx.Graph

the initial graph

weightstr, optional

the key in graph to use as weight. Default to ‘weight’

Returns
gnetworkx.Graph

a networkx graph where nodes are the parts

Examples

>>> n = 5
>>> g = nx.complete_graph(2*n)
>>> part = dict([])
>>> for node in g.nodes() :
>>>     part[node] = node % 2
>>> ind = induced_graph(part, g)
>>> goal = nx.Graph()
>>> goal.add_weighted_edges_from([(0,1,n*n),(0,0,n*(n-1)/2), (1, 1, n*(n-1)/2)])  # NOQA
>>> nx.is_isomorphic(ind, goal)
True
community.load_binary(data)

Load binary graph as used by the cpp implementation of this algorithm

community.modularity(partition, graph, weight='weight')

Compute the modularity of a partition of a graph

Parameters
partitiondict

the partition of the nodes, i.e a dictionary where keys are their nodes and values the communities

graphnetworkx.Graph

the networkx graph which is decomposed

weightstr, optional

the key in graph to use as weight. Default to ‘weight’

Returns
modularityfloat

The modularity

Raises
KeyError

If the partition is not a partition of all graph nodes

ValueError

If the graph has no link

TypeError

If graph is not a networkx.Graph

References

structure in networks. Physical Review E 69, 26113(2004).

Examples

>>> import community as community_louvain
>>> import networkx as nx
>>> G = nx.erdos_renyi_graph(100, 0.01)
>>> partition = community_louvain.best_partition(G)
>>> modularity(partition, G)
community.partition_at_level(dendrogram, level)

Return the partition of the nodes at the given level

A dendrogram is a tree and each level is a partition of the graph nodes. Level 0 is the first partition, which contains the smallest communities, and the best is len(dendrogram) - 1. The higher the level is, the bigger are the communities

Parameters
dendrogramlist of dict

a list of partitions, ie dictionnaries where keys of the i+1 are the values of the i.

levelint

the level which belongs to [0..len(dendrogram)-1]

Returns
partitiondictionnary

A dictionary where keys are the nodes and the values are the set it belongs to

Raises
KeyError

If the dendrogram is not well formed or the level is too high

See also

best_partition

which directly combines partition_at_level and

generate_dendrogram

to obtain the partition of highest modularity

Examples

>>> G=nx.erdos_renyi_graph(100, 0.01)
>>> dendrogram = generate_dendrogram(G)
>>> for level in range(len(dendrogram) - 1) :
>>>     print("partition at level", level, "is", partition_at_level(dendrogram, level))  # NOQA

Indices and tables