Efficient Computation Of The Weighted Clustering Coefficient

The clustering coefficient of an unweighted network has been extensively used to quantify how tightly connected a neighbor is around a node, and it has been widely adopted for assessing the quality of nodes in a social network. The computation of the clustering coefficient is challenging because it requires counting the number of triangles in the graph. Several recent works have proposed efficient sampling, streaming, and MapReduce algorithms that make it possible to overcome this computational bottleneck.As a matter of fact, the intensity of the interaction between nodes, which is usually represented with weights on the edges of the graph, is also an important measure of the statistical cohesiveness of a network. Recently, various notions of weighted clustering coefficient have been proposed but all those techniques are hard to implement on large-scale graphs.In this work we show how standard sampling techniques can be used to obtain efficient estimators for the most commonly used measures of weighted clustering coefficient. Furthermore, we propose a novel graph-theoretic notion of clustering coefficient in weighted networks.