Clustering in Complex Directed Networks

Details Clustering in Complex Directed Networks Clustering in Complex Directed Networks

2006-12-18

arxiv.org/abs/physics/0612169v3

Physics

Physics and Society

Scientific paper

10.1103/PhysRevE.76.026107

Many empirical networks display an inherent tendency to cluster, i.e. to form circles of connected nodes. This feature is typically measured by the clustering coefficient (CC). The CC, originally introduced for binary, undirected graphs, has been recently generalized to weighted, undirected networks. Here we extend the CC to the case of (binary and weighted) directed networks and we compute its expected value for random graphs. We distinguish between CCs that count all directed triangles in the graph (independently of the direction of their edges) and CCs that only consider particular types of directed triangles (e.g., cycles). The main concepts are illustrated by employing empirical data on world-trade flows.

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