girvan_newman(G, most_valuable_edge=None)
The Girvan–Newman algorithm detects communities by progressively removing edges from the original graph. The algorithm removes the "most valuable" edge, traditionally the edge with the highest betweenness centrality, at each step. As the graph breaks down into pieces, the tightly knit community structure is exposed and the result can be depicted as a dendrogram.
Function that takes a graph as input and outputs an edge. The edge returned by this function will be recomputed and removed at each iteration of the algorithm.
If not specified, the edge with the highest networkx.edge_betweenness_centrality
will be used.
Iterator over tuples of sets of nodes in G. Each set of node is a community, each tuple is a sequence of communities at a particular level of the algorithm.
Finds communities in a graph using the Girvan–Newman method.
>>> G = nx.path_graph(10) >>> comp = girvan_newman(G) >>> tuple(sorted(c) for c in next(comp)) ([0, 1, 2, 3, 4], [5, 6, 7, 8, 9])
>>> import itertools >>> G = nx.path_graph(8) >>> k = 2 >>> comp = girvan_newman(G) >>> for communities in itertools.islice(comp, k): ... print(tuple(sorted(c) for c in communities)) ... ([0, 1, 2, 3], [4, 5, 6, 7]) ([0, 1], [2, 3], [4, 5, 6, 7])
>>> import itertools >>> G = nx.path_graph(8) >>> k = 4 >>> comp = girvan_newman(G) >>> limited = itertools.takewhile(lambda c: len(c) <= k, comp) >>> for communities in limited: ... print(tuple(sorted(c) for c in communities)) ... ([0, 1, 2, 3], [4, 5, 6, 7]) ([0, 1], [2, 3], [4, 5, 6, 7]) ([0, 1], [2, 3], [4, 5], [6, 7])
>>> from operator import itemgetter
>>> G = nx.path_graph(10)
>>> edges = G.edges()
>>> nx.set_edge_attributes(G, {(u, v): v for u, v in edges}, "weight")
>>> def heaviest(G):
... u, v, w = max(G.edges(data="weight"), key=itemgetter(2))
... return (u, v)
...
>>> comp = girvan_newman(G, most_valuable_edge=heaviest)
>>> tuple(sorted(c) for c in next(comp))
([0, 1, 2, 3, 4, 5, 6, 7, 8], [9])>>> from networkx import edge_betweenness_centrality as betweenness >>> def most_central_edge(G): ... centrality = betweenness(G, weight="weight") ... return max(centrality, key=centrality.get) ... >>> G = nx.path_graph(10) >>> comp = girvan_newman(G, most_valuable_edge=most_central_edge) >>> tuple(sorted(c) for c in next(comp)) ([0, 1, 2, 3, 4], [5, 6, 7, 8, 9])
>>> from networkx import edge_betweenness_centrality
>>> from random import random
>>> def most_central_edge(G):
... centrality = edge_betweenness_centrality(G)
... max_cent = max(centrality.values())
... # Scale the centrality values so they are between 0 and 1,
... # and add some random noise.
... centrality = {e: c / max_cent for e, c in centrality.items()}
... # Add some random noise.
... centrality = {e: c + random() for e, c in centrality.items()}
... return max(centrality, key=centrality.get)
...
>>> G = nx.path_graph(10)
>>> comp = girvan_newman(G, most_valuable_edge=most_central_edge)Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them