Measuring the Clustering Strength of a Network via the Normalized Clustering Coefficient
arXiv:1908.00523
The paper introduces a normalized clustering coefficient that adjusts the traditional clustering measure to be robust against network size, density, and degree heterogeneity, and demonstrates its theoretical properties and practical uses in clustering, sampling, and dynamic analysis of networks.
Abstract
In this paper, we propose a novel statistic of networks, the normalized clustering coefficient, which is a modified version of the clustering coefficient that is robust to network size, network density and degree heterogeneity under different network generative models. In particular, under the degree corrected block model (DCBM), the "in-out-ratio" could be inferred from the normalized clustering coefficient. Asymptotic properties of the proposed 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 data analysis are carried out to demonstrate these applications.