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:	graph : networkx.Graph the networkx graph which is decomposed partition : dict, optional the algorithm will start using this partition of the nodes. It’s a dictionary where keys are their nodes and values the communities weight : str, optional the key in graph to use as weight. Default to ‘weight’ resolution : double, 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 randomize : boolean, optional Will randomize the node evaluation order and the community evaluation order to get different partitions at each call random_state : int, 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:	partition : dictionnary The partition, with communities numbered from 0 to number of communities
Raises:	NetworkXError If the graph is not undirected.

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:	graph : networkx.Graph the networkx graph which will be decomposed part_init : dict, optional the algorithm will start using this partition of the nodes. It’s a dictionary where keys are their nodes and values the communities weight : str, optional the key in graph to use as weight. Default to ‘weight’ resolution : double, 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:	dendrogram : list 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:	partition : dict a dictionary where keys are graph nodes and values the part the node belongs to graph : networkx.Graph the initial graph weight : str, optional the key in graph to use as weight. Default to ‘weight’
Returns:	g : networkx.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:	partition : dict the partition of the nodes, i.e a dictionary where keys are their nodes and values the communities graph : networkx.Graph the networkx graph which is decomposed weight : str, optional the key in graph to use as weight. Default to ‘weight’
Returns:	modularity : float 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:	dendrogram : list of dict a list of partitions, ie dictionnaries where keys of the i+1 are the values of the i. level : int the level which belongs to [0..len(dendrogram)-1]
Returns:	partition : dictionnary 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

Indices and tables¶

Community detection for NetworkX’s documentation¶

This module implements community detection.

It uses the louvain method described in Fast unfolding of communities in large networks, Vincent D Blondel, Jean-Loup Guillaume, Renaud Lambiotte, Renaud Lefebvre, Journal of Statistical Mechanics: Theory and Experiment 2008(10), P10008 (12pp)

It depends on Networkx to handle graph operations : http://networkx.lanl.gov/

The program can be found in a repository where you can also report bugs :

https://github.com/taynaud/python-louvain

Example :¶

As a command line utility :¶

You should consider using the cpp version at http://findcommunities.googlepages.com/ !

./community.py file.bin > tree

where file.bin is a binary graph as generated by the convert utility of the cpp version.

The generated file can then be used with the hierarchy utility of the cpp version. Note that the program does not make many verifications about the arguments, and is expecting a friendly use.

As python module :¶

import community as community_louvain
import matplotlib.cm as cm
import matplotlib.pyplot as plt
import networkx as nx

# load the karate club graph
G = nx.karate_club_graph()

#first 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()

Changelog :¶

2020-12-27 : 0.16, Fix when using the resolution parameter. Doc fixes
2020-12-27 : 0.15, Stop relabelling stable partitions, tests on power, doc fixes
2020-04-06 : 0.14, bugfixes (on resolution parameter), optimization on random state
2018-12-21 : 0.13, better random state, some files missing included, communities always in 0..N-1
2018-05-22 : 0.11, stop forcing networkx<2.0 and expose module __version__
2018-01-02 : 0.10, bug fix: taking into account the node removal cost
2017-09-21 : 0.9, support networkx 2.0
2017-06-03 : 0.8, add randomization and bugfixes
2017-05-21 : 0.7, migrate to github, readthedocs and travis. Add resolution parameter to control community size, bugfixes
04/21/2011 : modifications to use networkx like documentation and use of test.
02/22/2011 : correction of a bug regarding edge weights
01/14/2010 : modification to use networkx 1.01 graph api and adding the possibility to start the algorithm with a given partition
04/10/2009 : increase of the speed of the detection by caching node degrees

License :¶

Copyright (c) 2009, Thomas Aynaud <thomas.aynaud@lip6.fr>
All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

* Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

* Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

* Neither the name of the python-louvain Developers nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.