The Index-based Subgraph Matching Algorithm with General Symmetries (ISMAGS): exploiting symmetry for faster subgraph enumeration.

Maarten Houbraken,Sofie Demeyer,Tom Michoel,Didier Colle,Mario Pickavet,Pieter Audenaert,Peter Csermely

doi:10.1371/journal.pone.0097896

Maarten Houbraken, Sofie Demeyer + Show 5 more

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https://doi.org/10.1371/journal.pone.0097896

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Abstract

Subgraph matching algorithms are used to find and enumerate specific interconnection structures in networks. By enumerating these specific structures/subgraphs, the fundamental properties of the network can be derived. More specifically in biological networks, subgraph matching algorithms are used to discover network motifs, specific patterns occurring more often than expected by chance. Finding these network motifs yields information on the underlying biological relations modelled by the network. In this work, we present the Index-based Subgraph Matching Algorithm with General Symmetries (ISMAGS), an improved version of the Index-based Subgraph Matching Algorithm (ISMA). ISMA quickly finds all instances of a predefined motif in a network by intelligently exploring the search space and taking into account easily identifiable symmetric structures. However, more complex symmetries (possibly involving switching multiple nodes) are not taken into account, resulting in superfluous output. ISMAGS overcomes this problem by using a customised symmetry analysis phase to detect all symmetric structures in the network motif subgraphs. These structures are then converted to symmetry-breaking constraints used to prune the search space and speed up calculations. The performance of the algorithm was tested on several types of networks (biological, social and computer networks) for various subgraphs with a varying degree of symmetry. For subgraphs with complex (multi-node) symmetric structures, high speed-up factors are obtained as the search space is pruned by the symmetry-breaking constraints. For subgraphs with no or simple symmetric structures, ISMAGS still reduces computation times by optimising set operations. Moreover, the calculated list of subgraph instances is minimal as it contains no instances that differ by only a subgraph symmetry. An implementation of the algorithm is freely available at https://github.com/mhoubraken/ISMAGS.

Highlights

In modern society, technology has been applied to create and study numerous advanced systems in various fields as biology, sociology, informatics and others
We introduce the Index-based Subgraph Matching Algorithm with General Symmetries (ISMAGS) in which search space size and query times are further reduced by incorporating the internal symmetry of subgraphs as constraints into the algorithm
After a description of the algorithms and network data use, ISMAGS is compared against it predecessor ISMA to show the effects of the added symmetry breaking and related optimisations

Summary

Introduction

Technology has been applied to create and study numerous advanced systems in various fields as biology, sociology, informatics and others To understand their internal dynamics, many of these systems can be modelled using graph theory. A powerful analysis technique is described in [1] and consists of finding network motifs in the graph These network motifs denote small interactions patterns between several proteins that are unusually more present in the graph than expected by chance. They can be modelled as small subgraphs which can be searched in the larger network representing all known interactions between all proteins. By discovering these network motifs, our understanding of the underlying mechanisms of the network can be improved

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