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.
Highlights
Network analysis is concerned with finding patterns and anomalies in real-world graphs, such as social networks, computer and communication networks, or biological and ecological processes
We show the unnormalised Complementary Cumulative Distribution Function (CCDF) in our plots; the normalised value can be obtained by integrating the area under the curve to 1
We presented AGWAN, a generative model for random graphs with discrete labels and weighted edges
Summary
Network analysis is concerned with finding patterns and anomalies in real-world graphs, such as social networks, computer and communication networks, or biological and ecological processes. AGWAN (Attribute Graph: Weighted and Numeric), represents the distribution of edge weights as Beta Mixture Models (BMMs) which are learned from weighted input graphs. This paper is arranged as follows: Section 2 is an overview of generative graph models and approaches to estimating mixture model parameters; Section 3 presents AGWAN, our generative model for weighted and numeric labelled graphs, including our algorithm for fitting AGWAN’s parameters to real input graphs.
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