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Abstract

Nodes in real-world networks tend to cluster into densely connected groups, a property captured by the clustering coefficient. It was however initially defined for unweighted and undirected networks, which left out crucial information about dynamics on weighted graphs. Several generalizations have therefore been proposed for weighted networks. However, none of them fulfills the continuity condition: edges with vanishing weights have an impact that differs from the absence of an edge. We propose here a new definition of the clustering coefficient that tackles this issue while satisfying previously formulated requirements. This new definition is less sensitive to weak spurious connections that can be generated by noise or statistical biases. Compared to previous methods, it is thus able to detect topological features more precisely and behaves in a more sensible manner for inferred networks. Finally we discuss the differences between clustering methods on several real-world graphs, notably weighted and directed brain networks.