Sampling Graphlets of Multiplex Networks: A Restricted Random Walk Approach

Abstract

Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of effort has been devoted to calculating graphlet statistics where random walk-based approaches are commonly used to access restricted graphs through the available application programming interfaces (APIs). However, most of them merely consider individual networks while overlooking the strong coupling between different networks. In this article, we estimate the graphlet concentration in multiplex networks with real-world applications. An inter-layer edge connects two nodes in different layers if they actually belong to the same node. The access to a multiplex network is restrictive in the sense that the upper layer allows random walk sampling, whereas the nodes of lower layers can be accessed only through the inter-layer edges and only support random node or edge sampling. To cope with this new challenge, we define a suit of two-layer graphlets and propose novel random walk sampling algorithms to estimate the proportion of all the three-node graphlets. An analytical bound on the sampling steps is proved to guarantee the convergence of our unbiased estimator. We further generalize our algorithm to explore the tradeoff between the estimated accuracy of different graphlets when the sample budget is split into different layers. Experimental evaluation on real-world and synthetic multiplex networks demonstrates the accuracy and high efficiency of our unbiased estimators.