A measure for the cohesion of weighted networks

A generalization of both the Botafogo-Rivlin-Shneiderman compactness measure and the Wiener index is presented. These new measures for the cohesion of networks can be used in case a dissimilarity value is given between nodes in a network or a graph. It is illustrated how a set of weights between connected nodes can be transformed into a set of dissimilarity measures for all nodes. The new compactness measure for the cohesion of weighted graphs has several desirable properties related to the disjoint union of two networks. Finally, an example is presented of the calculation of the new compactness measures for a co-citation and a bibliographic coupling network.