An analytic derivation of clustering coefficients for weighted networks

Clustering coefficients are among the most important parameters characterizing the topology of complex networks and have a significant influence on various dynamical processes occurring on networks. On the other hand, a plethora of real-life networks with diverse links can be described better in terms of weighted networks than in terms of binary networks, where all links are homogeneous. However, analytical research on clustering coefficients in weighted networks is still lacking. In this paper, we apply an extended mean-field approach to investigate clustering coefficients for the typical weighted networks proposed by Barrat, Barthélemy and Vespignani (BBV networks) (2004 Phys. Rev. Lett. 92 228701). We provide an analytical solution to the model, showing how the local clustering of a node in the BBV networks depends on its degree and strength. Our analysis is in good agreement with the results of numerical simulations