community API

This package implements community detection.

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

See also

best_partition, generate_dendrogram

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

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

>>> G=nx.erdos_renyi_graph(100, 0.01)
>>> part = best_partition(G)
>>> modularity(part, G)

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

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

Returns:

partition : dictionnary

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

Raises:

NetworkXError :

If the graph is not Eulerian.

See also

generate_dendrogram

Notes

Uses Louvain algorithm

References

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

Examples

>>>  #Basic usage
>>> G=nx.erdos_renyi_graph(100, 0.01)
>>> part = best_partition(G)

>>> #other example to display a graph with its community :
>>> #better with karate_graph() as defined in networkx examples
>>> #erdos renyi don't have true community structure
>>> G = nx.erdos_renyi_graph(30, 0.05)
>>> #first compute the best partition
>>> partition = community.best_partition(G)
>>>  #drawing
>>> size = float(len(set(partition.values())))
>>> pos = nx.spring_layout(G)
>>> count = 0.
>>> for com in set(partition.values()) :
>>>     count += 1.
>>>     list_nodes = [nodes for nodes in partition.keys()
>>>                                 if partition[nodes] == com]
>>>     nx.draw_networkx_nodes(G, pos, list_nodes, node_size = 20,
                                node_color = str(count / size))
>>> nx.draw_networkx_edges(G,pos, alpha=0.5)
>>> plt.show()

community.generate_dendrogram(graph, part_init=None, weight='weight', resolution=1.0)

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(int, goal)
True

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