Generating Realistic Labelled, Weighted Random Graphs †

Algorithms

Michael Charles Davis⁴  Zhanyu Ma²  Weiru Liu³  Paul Miller³  Ruth Hunter¹  Frank Kee¹ 

[1] Centre for Public Health, Queen’s University Belfast, University Road, Belfast BT7 1NN, UK; E-Mails:;Pattern Recognition and Intelligent Systems (PRIS) Lab, Beijing University of Posts and Telecommunications (BUPT), 100876 Beijing, China;School of Electrical and Electronic Engineering and Computer Science, Queen’s University Belfast, University Road, Belfast BT7 1NN, UK; E-Mails:;Organisation Européene pour la Recherche Nucléaire (CERN), Route de Meyrin 385, 1217 Meyrin, Switzerland

关键词: network models;    generative algorithms;    random graphs;    labelled graphs;    weighted graphs;    bayesian estimation;    maximum likelihood estimation;    beta distribution;    mixture modeling;    variational inference;   

DOI  :  10.3390/a8041143

来源: mdpi

【 摘 要 】

Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs) with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI) approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs). Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.