From which world is your graph?

TL;DR

This paper introduces a unified, statistically sound polynomial-time algorithm capable of uncovering latent structures in sparse graphs, effectively distinguishing between stochastic blockmodels and small world models.

Contribution

It unifies two major link-formation models using advanced techniques, providing the first efficient method to identify latent patterns in sparse networks for both models.

Findings

Successfully identifies block structures in SBMs

Accurately estimates latent positions in SWMs

Operates efficiently on sparse graphs

Abstract

Discovering statistical structure from links is a fundamental problem in the analysis of social networks. Choosing a misspecified model, or equivalently, an incorrect inference algorithm will result in an invalid analysis or even falsely uncover patterns that are in fact artifacts of the model. This work focuses on unifying two of the most widely used link-formation models: the stochastic blockmodel (SBM) and the small world (or latent space) model (SWM). Integrating techniques from kernel learning, spectral graph theory, and nonlinear dimensionality reduction, we develop the first statistically sound polynomial-time algorithm to discover latent patterns in sparse graphs for both models. When the network comes from an SBM, the algorithm outputs a block structure. When it is from an SWM, the algorithm outputs estimates of each node's latent position.