  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.
