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Algorithms 2015, 8(4), 1143-1174; doi:10.3390/a8041143

Generating Realistic Labelled, Weighted Random Graphs

1
Organisation Européene pour la Recherche Nucléaire (CERN), Route de Meyrin 385, 1217 Meyrin, Switzerland
2
Pattern Recognition and Intelligent Systems (PRIS) Lab, Beijing University of Posts and Telecommunications (BUPT), 100876 Beijing, China
3
School of Electrical and Electronic Engineering and Computer Science, Queen’s University Belfast, University Road, Belfast BT7 1NN, UK
4
Centre for Public Health, Queen’s University Belfast, University Road, Belfast BT7 1NN, UK
This paper is an extended version of our paper published in New Frontiers in Mining Complex Patterns—Second International Workshop (NFMCP 2013), held in conjunction with the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML/PKDD 2013), Prague, Czech Republic, 27 September 2013.
*
Authors to whom correspondence should be addressed.
Academic Editor: Maurizio Patrignani
Received: 1 June 2015 / Revised: 16 November 2015 / Accepted: 20 November 2015 / Published: 8 December 2015
(This article belongs to the Special Issue Graph Drawing and Experimental Algorithms)
View Full-Text   |   Download PDF [1137 KB, uploaded 8 December 2015]   |  

Abstract

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. View Full-Text
Keywords: network models; generative algorithms; random graphs; labelled graphs; weighted graphs; bayesian estimation; maximum likelihood estimation; beta distribution; mixture modeling; variational inference network models; generative algorithms; random graphs; labelled graphs; weighted graphs; bayesian estimation; maximum likelihood estimation; beta distribution; mixture modeling; variational inference
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Davis, M.C.; Ma, Z.; Liu, W.; Miller, P.; Hunter, R.; Kee, F. Generating Realistic Labelled, Weighted Random Graphs. Algorithms 2015, 8, 1143-1174.

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