Multi-group connectivity structures and their implications

TL;DR

This paper explores various multi-group connectivity structures in networks, proposing generative models and analyzing their effects on information flow, consensus speed, and stability under noise, with implications for understanding complex network behaviors.

Contribution

It introduces new generative models for four types of multi-group connectivity and provides a comparative analysis of their impact on network dynamics.

Findings

Different connectivity modalities influence information propagation rates.

Connectivity structures affect convergence times to consensus.

Network size impacts steady state deviations under noise.

Abstract

We investigate the implications of different forms of multi-group connectivity. Four multi-group connectivity modalities are considered: co-memberships, edge bundles, bridges, and liaison hierarchies. We propose generative models to generate these four modalities. Our models are variants of planted partition or stochastic block models conditioned under certain topological constraints. We report findings of a comparative analysis in which we evaluate these structures, controlling for their edge densities and sizes, on mean rates of information propagation, convergence times to consensus, and steady state deviations from the consensus value in the presence of noise as network size increases.