Girvan–Newman algorithm: Difference between revisions

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The Girvan–Newman algorithm detects communities by progressively removing edges from the original network. The connected components of the remaining network are the communities. Instead of trying to construct a measure that tells us which edges are the most central to communities, the Girvan–Newman algorithm focuses on edges that are most likely "between" communities.

[[Betweenness centrality|Vertex betweenness]] hasis beenan studied in the past as a measureindicator of thehighly [[centrality|central]] and influence of nodes in networks. For any node <math>i</math>, vertex betweenness is defined as the number of shortest paths between pairs of nodes that run through it. It is arelevant measureto ofmodels where the influencenetwork ofmodulates a node over the flowtransfer of informationgoods between otherknown nodes,start especiallyand inend casespoints, whereunder informationthe flowassumption overthat asuch networktransfer primarily followsseeks the shortest available pathroute.

The Girvan–Newman algorithm extends this definition to the case of edges, defining the "edge betweenness" of an edge as the number of shortest paths between pairs of nodes that run along it. If there is more than one shortest path between a pair of nodes, each path is assigned equal weight such that the total weight of all of the paths is equal to unity. If a network contains communities or groups that are only loosely connected by a few inter-group edges, then all shortest paths between different communities must go along one of these few edges. Thus, the edges connecting communities will have high edge betweenness (at least '''one''' of them). By removing these edges, the groups are separated from one another and so the underlying community structure of the network is revealed.

The algorithm's steps for community detection are summarized below