Intensity and coherence of motifs in weighted complex networks

Details Intensity and coherence of motifs in weighted complex networks Intensity and coherence of motifs in weighted complex networks

2004-08-28

arxiv.org/abs/cond-mat/0408629v3

Phys. Rev. E 71, 065103 (2005)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures, uses REVTeX4; minor errors corrected, certain points clarified

Scientific paper

10.1103/PhysRevE.71.065103

The local structure of unweighted networks can be characterized by the number of times a subgraph appears in the network. The clustering coefficient, reflecting the local configuration of triangles, can be seen as a special case of this approach. In this Letter we generalize this method for weighted networks. We introduce subgraph intensity as the geometric mean of its link weights and coherence as the ratio of the geometric to the corresponding arithmetic mean. Using these measures, motif scores and clustering coefficient can be generalized to weighted networks. To demonstrate these concepts, we apply them to financial and metabolic networks and find that inclusion of weights may considerably modify the conclusions obtained from the study of unweighted characteristics.

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