Networks with arbitrary edge multiplicities

Abstract

One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of triangles in which edges, rather than vertices, participate. Here we show that the multiplicity distribution of real networks is in many cases scale-free, and in general very broad. Thus, besides the fact that in real networks the number of edges attached to vertices often has a scale-free distribution, we find that the number of triangles attached to edges can have a scale-free distribution as well. We show that current models, even when they generate clustered networks, systematically fail to reproduce the observed multiplicity distributions. We therefore propose a generalized model that can reproduce networks with arbitrary distributions of vertex degrees and edge multiplicities, and study many of its properties analytically.

References in corpus (15)

• Community detection in graphs
• The Rich-Club Phenomenon In The Internet Topology
• Random graphs with clustering
• The entropy of randomized network ensembles
• Analytical maximum-likelihood method to detect patterns in real networks
• Random graphs containing arbitrary distributions of subgraphs
• Percolation and Epidemic Thresholds in Clustered Networks
• Clustering in complex networks. I. General formalism
• Generalized Bose-Fermi statistics and structural correlations in weighted networks
• Clustering in complex networks. II. Percolation properties
• Bond percolation on a class of clustered random networks
• On the rich-club effect in dense and weighted networks
• Topologically biased random walk with application for community finding in networks
• Phase transitions in social networks
• Generating random networks with given degree-degree correlations and degree-dependent clustering

Cited by in corpus (12)

• The Kuramoto model in complex networks
• The robustness of interdependent clustered networks
• Clustering implies geometry in networks
• Deciphering the global organization of clustering in real complex networks
• Latent geometry of bipartite networks
• Evolution of the Internet k-dense structure
• General and exact approach to percolation on random graphs
• Bond percolation on a class of correlated and clustered random graphs
• Percolation on random networks with arbitrary k-core structure
• Tweaking Synchronisation by Link Addition
• Color-avoiding percolation
• Spectra of random networks in the weak clustering regime