A simple bipartite graph projection model for clustering in networks release_lwexjuwsbncellyq4ie36theui

by Austin R. Benson, Paul Liu, Hao Yin

Released as a article .

2020  

Abstract

Graph datasets are frequently constructed by a projection of a bipartite graph, where two nodes are connected in the projection if they share a common neighbor in the bipartite graph; for example, a coauthorship graph is a projection of an author-publication bipartite graph. Analyzing the structure of the projected graph is common, but we do not have a good understanding of the consequences of the projection on such analyses. Here, we propose and analyze a random graph model to study what properties we can expect from the projection step. Our model is based on a Chung-Lu random graph for constructing the bipartite representation, which enables us to rigorously analyze the projected graph. We show that common network properties such as sparsity, heavy-tailed degree distributions, local clustering at nodes, the inverse relationship between node degree, and global transitivity can be explained and analyzed through this simple model. We also develop a fast sampling algorithm for our model, which we show is provably optimal for certain input distributions. Numerical simulations where model parameters come from real-world datasets show that much of the clustering behavior in some datasets can just be explained by the projection step.
In text/plain format

Archived Files and Locations

application/pdf  468.3 kB
file_mvevw5ugjbdszhilokdgsaq6nq
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2020-07-01
Version   v1
Language   en ?
arXiv  2007.00761v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 3aadba5d-6ef9-4695-addd-61e8aed8b3bb
API URL: JSON