A way to measure the community structure of a network is the clusteringcoefficient. Such a quantity is based on the number of existing trianglesaround the nodes over the theoretical ones. To the best of our knowledge,scarce attention has been paid to the fictitious triangles due to the presenceof indirect connections among the nodes of the network. This paper fills thisgap by providing a new definition of the clustering coefficient for weightednetworks when missing links might be also considered. Specifically, a novelconcept of triangles is here introduced by assuming that a strong enoughaggregate weight of two arcs sharing a node induces a link between the notcommon nodes. Beyond the intuitive meaning of such social triangles, we alsoexplore the usefulness of them for gaining insights on the topologicalstructure of the underline network. Empirical experiments on the standardnetworks of 500 commercial US airports and on the nervous system of theCaenorhabditis elegans support the theoretical framework.
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