Subgraph Similarity Search in Large Graphs

TL;DR

This paper presents an efficient algorithm for subgraph similarity search in large, noisy, unlabeled graphs using graphlet kernels, capable of handling real-world social and biological networks.

Contribution

It introduces a novel method that maps local topological information to vectors and finds globally similar subgraphs, scalable to large networks.

Findings

Successfully tested on large real-world networks

Detects highly similar subgraphs efficiently

Implementation runs in about one second on a 32-core machine

Abstract

One of the major challenges in applications related to social networks, computational biology, collaboration networks etc., is to efficiently search for similar patterns in their underlying graphs. These graphs are typically noisy and contain thousands of vertices and millions of edges. In many cases, the graphs are unlabeled and the notion of similarity is also not well defined. We study the problem of searching an induced subgraph in a large target graph that is most similar to the given query graph. We assume that the query graph and target graph are undirected and unlabeled. We use graphlet kernels \cite{shervashidze2009efficient} to define graph similarity. Graphlet kernels are known to perform better than other kernels in different applications. Our algorithm maps topological neighborhood information of vertices in the query and target graphs to vectors. These local topological informations are then combined to find a target subgraph having highly similar global topology with the given query graph. We tested our algorithm on several real world networks such as facebook network, google plus network, youtube network, amazon network etc. Most of them contain thousands of vertices and million edges. Our algorithm is able to detect highly similar matches when queried in these networks. Our multi-threaded implementation takes about one second to find the match on a 32 core machine, excluding the time for one time preprocessing. Computationally expensive parts of our algorithm can be further scaled to standard parallel and distributed frameworks like map-reduce.