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arXiv · 1510.02215

Distributed Estimation of Graph 4-Profiles

Ethan R. Elenberg·Karthikeyan Shanmugam·Michael Borokhovich·Alexandros G. Dimakis
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Abstract

We present a novel distributed algorithm for counting all four-node induced subgraphs in a big graph. These counts, called the $4$-profile, describe a graph's connectivity properties and have found several uses ranging from bioinformatics to spam detection. We also study the more complicated problem of estimating the local $4$-profiles centered at each vertex of the graph. The local $4$-profile embeds every vertex in an $11$-dimensional space that characterizes the local geometry of its neighborhood: vertices that connect different clusters will have different local $4$-profiles compared to those that are only part of one dense cluster. Our algorithm is a local, distributed message-passing scheme on the graph and computes all the local $4$-profiles in parallel. We rely on two novel theoretical contributions: we show that local $4$-profiles can be calculated using compressed two-hop information and also establish novel concentration results that show that graphs can be substantially sparsified and still retain good approximation quality for the global $4$-profile. We empirically evaluate our algorithm using a distributed GraphLab implementation that we scaled up to $640$ cores. We show that our algorithm can compute global and local $4$-profiles of graphs with millions of edges in a few minutes, significantly improving upon the previous state of the art.

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Ethan R. Elenberg, Karthikeyan Shanmugam, Michael Borokhovich, Alexandros G. Dimakis. 2015-10-08. Distributed Estimation of Graph 4-Profiles. https://arxiv.org/abs/1510.02215

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