Subgraph Matching on Multiplex Networks

Abstract

An active area of research in computational science is the design of algorithms for solving the subgraph matching problem to find copies of a given template graph in a larger world graph. Prior works have largely addressed single-channel networks using a variety of approaches. We present a suite of filtering methods for subgraph isomorphisms for multiplex networks (with different types of edges between nodes and more than one edge within each channel type). We aim to understand the entire solution space rather than focusing on finding one isomorphism. Results are shown on several classes of datasets: (a) Sudoku puzzles mapped to the subgraph isomorphism problem, (b) Erd ős-R ényi multigraphs, (c) real-world datasets from Twitter and transportation networks, (d) synthetic data created for the DARPA MAA program.

Structural Equivalence in Subgraph Matching

“…This paper takes inspiration for the general subgraph tree search structure from [51] and shares many of the same test cases on multichannel networks. In our previous work [42], we introduced a simpler notion of candidate equivalence and candidate structure, and tested it on a small selection of multichannel networks.…”

“…An alternate notion of equivalence, introduced in [51], involves the use of a node cover. A node cover is a subset of nodes whose removal, along with incident edges, results in a completely disconnected graph.…”

“…A node cover is a subset of nodes whose removal, along with incident edges, results in a completely disconnected graph. The approach in [51] is to build up a partial match of all the vertices in the node cover followed by assigning all the nodes outside the node cover. After reducing the candidate sets of all the nodes outside the cover to those that have enough connections to the nodes in the cover, what remains is to ensure that they are all different.…”

“…This problem has been well-studied especially in the pattern recognition community. The surveys [20], [9], and [28] explain the broad variety of techniques used as well as applications including handwriting recognition [2], face recognition [4], biomedical uses [3], sudoku puzzles and adversarial activity [51]. More recently, subgraph matching arises as a component in motif discovery [23], [37], where frequent subgraphs are uncovered for graph analysis in domains including social networks and biochemical data.…”

“…We are interested in the subgraph matching problem (SMP) [51]: Definition 2 (Subgraph Matching Problem). Given a template graph G T and a world graph G W , find all subgraph isomorphisms from G T to G W .…”