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In this paper, we propose a novel statistic of networks, the normalizedclustering coefficient, which is a modified version of the clusteringcoefficient that is robust to network size, network density and degreeheterogeneity under different network generative models. In particular, underthe degree corrected block model (DCBM), the "in-out-ratio" could be inferredfrom the normalized clustering coefficient. Asymptotic properties of theproposed indicator are studied under three popular network generative models.The normalized clustering coefficient can also be used for networks clustering,network sampling as well as dynamic network analysis. Simulations and real dataanalysis are carried out to demonstrate these applications.

Measuring the Clustering Strength of a Network via the Normalized Clustering Coefficient