Social triangles and generalized clustering coefficient for weighted networks

In the context of expert systems approach, the problem of community detection can be afford as a clustering model for networks. In this respect, a way to measure the community structure is the clustering coefficient. Such a quantity is based on the number of existing triangles around the nodes over the theoretical ones. To the best of our knowledge, scarce attention has been paid to the fictitious triangles due to the presence of indirect connections among the nodes of the network. This paper fills this gap by providing a new definition of the clustering coefficient for weighted networks when missing links might be also considered. Specifically, a novel concept of triangles is here introduced by assuming that a strong enough aggregate weight of two arcs sharing a node induces a link between the not common nodes. Beyond the intuitive meaning of such social triangles, we also explore the usefulness of them for gaining insights on the topological structure of the underline network. Empirical experiments on the standard networks of 500 commercial US airports and on the nervous system of the Caenorhabditis elegans support the theoretical framework. ∗Corresponding author.