Strength of a graph

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In graph theory, the strength of an undirected graph corresponds to the minimum ratio of edges removed/components created in a decomposition of the graph in question. It is a method to compute partitions of the set of vertices and detect zones of high concentration of edges, and is analogous to graph toughness which is defined similarly for vertex removal.

Definitions

The strength \sigma(G) of an undirected simple graph G = (V, E) admits the three following definitions:

Complexity

Computing the strength of a graph can be done in polynomial time, and the first such algorithm was discovered by Cunningham (1985). The algorithm with best complexity for computing exactly the strength is due to Trubin (1993), uses the flow decomposition of Goldberg and Rao (1998), in time.

Properties

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