Stochastic Block Models are a Discrete Surface Tension

TL;DR

This paper reveals that maximum likelihood estimation in stochastic block models is analogous to a continuum surface-tension problem, connecting network clustering to physical surface phenomena, and demonstrates this analogy through algorithms and empirical network analysis.

Contribution

It establishes a novel connection between stochastic block models and surface tension problems, introducing network analogs of surface-tension algorithms for community detection.

Findings

Successfully recovered planted community structures in synthetic networks.

Provided insights into empirical networks from hyperspectral videos.

Demonstrated the utility of surface-tension algorithms in network analysis.

Abstract

Networks, which represent agents and interactions between them, arise in myriad applications throughout the sciences, engineering, and even the humanities. To understand large-scale structure in a network, a common task is to cluster a network's nodes into sets called "communities", such that there are dense connections within communities but sparse connections between them. A popular and statistically principled method to perform such clustering is to use a family of generative models known as stochastic block models (SBMs). In this paper, we show that maximum likelihood estimation in an SBM is a network analog of a well-known continuum surface-tension problem that arises from an application in metallurgy. To illustrate the utility of this relationship, we implement network analogs of three surface-tension algorithms, with which we successfully recover planted community structure in synthetic networks and which yield fascinating insights on empirical networks that we construct from hyperspectral videos.