Subnetwork enumeration algorithms for multilayer networks

TL;DR

This paper generalizes subnetwork enumeration algorithms for multilayer networks, enabling unbiased sampling and parallelization, thus facilitating advanced analysis of complex multilayer network data.

Contribution

It introduces two new algorithms for subnetwork enumeration in multilayer networks that maintain unbiased sampling and are suitable for parallel computing.

Findings

Algorithms perform similarly in efficiency depending on data features.

General algorithms enable analysis of complex multilayer networks.

Evaluation on synthetic and real data demonstrates practical applicability.

Abstract

To understand the structure of a network, it can be useful to break it down into its constituent pieces. This is the approach taken in a multitude of successful network analysis methods, such as motif analysis. These methods require one to enumerate or sample small connected subgraphs of a network, which can be computationally intractable if naive methods are used. Efficient algorithms exists for both enumeration and uniform sampling of subgraphs, and here we generalize the ESU algorithm for a very general notion of multilayer networks. We show that multilayer network subnetwork enumeration introduces nontrivial complications to the existing algorithm, and present two different generalized algorithms that preserve the desired features of unbiased sampling and trivial parallelization. We evaluate these algorithms in synthetic networks and with real-world data, and show that neither of the algorithms is strictly more efficient but rather the choice depends on the features of the data. Having a general algorithm for finding subnetworks makes advanced multilayer network analysis possible, and enables researchers to apply a variety of methods to previously difficult-to-handle multilayer networks in a variety of domains and across many different types of multilayer networks.