A generalised clustering coefficient quantifying long range clustering of networks

The study of the clustering property of real world networks has focused mainly on measuring the ratio of the number of triangles over the number of connected triplets of vertices (clustering coefficient). Many real world networks have high values of this type of clustering. We argue that the quantification of higher order clustering provides complementary information on the structure of real world networks. To quantify higher order clustering, we propose the generalised clustering coefficient which can be computed efficiently as it is expressed in terms of the adjacency matrix exponential. Based on the generalised clustering coefficient we introduce the clustering signature plot which characterises the clustering structure of networks. We use the proposed plot to analyse the clustering of different order, of social networks and other real world networks.