2006/08/15 by M. Angeles Serrano, M. Ángeles Serrano, Marian Boguna +1 · 1 citation
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Topological and Geometric Data Analysis #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.74.056114
published as Physical Review E 74, 056114 (2006)
arxiv created 2006/08/15 · openalex publication_date 2006/11/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in that it involves the properties of two-and not just one-vertices. The formalism is completed with the definition of a three-vertex correlation function, which is the fundamental quantity describing the properties of clustered networks. The formalism suggests different metrics that are able to thoroughly characterize transitive relations. A rigorous analysis of several real networks, which makes use of this formalism and the metrics, is also provided. It is also found that clustered networks can be classified into two main groups: the weak and the strong transitivity classes. In the first class, edge multiplicity is small, with triangles being disjoint. In the second class, edge multiplicity is high and so triangles share many edges. As we shall see in the following paper, the class a network belongs to has strong implications in its percolation properties.