Alignment and Comparison of Directed Networks via Transition Couplings of Random Walks

TL;DR

NetOTC is a transport-based method for comparing and aligning directed and undirected networks by coupling their random walks, capturing both local and global network features without parameters or randomization.

Contribution

The paper introduces NetOTC, a novel transport-based approach for network comparison and alignment that handles various network types and preserves edge information.

Findings

NetOTC effectively quantifies network differences.

It provides meaningful alignments of vertices and edges.

The method demonstrates strong empirical performance.

Abstract

We describe and study a transport based procedure called NetOTC (network optimal transition coupling) for the comparison and alignment of two networks. The networks of interest may be directed or undirected, weighted or unweighted, and may have distinct vertex sets of different sizes. Given two networks and a cost function relating their vertices, NetOTC finds a transition coupling of their associated random walks having minimum expected cost. The minimizing cost quantifies the difference between the networks, while the optimal transport plan itself provides alignments of both the vertices and the edges of the two networks. Coupling of the full random walks, rather than their marginal distributions, ensures that NetOTC captures local and global information about the networks, and preserves edges. NetOTC has no free parameters, and does not rely on randomization. We investigate a number of theoretical properties of NetOTC and present experiments establishing its empirical performance.