Girvan–Newman algorithm: Difference between revisions

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{{short description|Community detection algorithm}}

The '''Girvan–Newman algorithm''' (named after [[Michelle Girvan]] and [[Mark Newman]]) is a hierarchical method used to detect [[Community structure|communities]] in [[complex system]]s.<ref name=newman>Girvan M. and Newman M. E. J., [httphttps://dx.doi.org/10.1073/pnas.122653799 Community structure in social and biological networks], Proc. Natl. Acad. Sci. USA '''99''', 7821–7826 (2002)</ref>

== Edge betweenness and community structure ==

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]] is an indicator of highly [[centrality|central]] nodes in networks. For any node <math>i</math>, vertex betweenness is defined as the numberfraction of shortest paths between pairs of nodes that run through it. It is relevant to models where the network modulates transfer of goods between known start and end points, under the assumption that such transfer seeks the shortest available route.

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.

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# The betweenness of all existing edges in the network is calculated first.

# The edge(s) with the highest betweenness isare removed.

# The betweenness of all edges affected by the removal is recalculated.

# Steps 2 and 3 are repeated until no edges remain.

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== See also ==

* [[Betweenness]]

* [[Closeness (mathematics)|Closeness]]

* [[Hierarchical clustering]]