Distributions of Centrality on Networks
For researchers and practitioners using random network models, this work provides theoretical guarantees and practical tools to compute centralities, addressing a gap between deterministic centrality theory and stochastic network practice.
This paper provides a framework for determining centralities in large random networks, proving that centrality measures concentrate around their expected values. Applications to stochastic block models, geographic networks, and multi-characteristic networks show how network structure drives inequality and peer effect benefits.
We provide a framework for determining the centralities of agents in a broad family of random networks. Current understanding of network centrality is largely restricted to deterministic settings, but practitioners frequently use random network models to accommodate data limitations or prove asymptotic results. Our main theorems show that on large random networks, centrality measures are close to their expected values with high probability. We illustrate the economic consequences of these results by presenting three applications: (1) In network formation models based on community structure (called stochastic block models), we show network segregation and differences in community size produce inequality. Benefits from peer effects tend to accrue disproportionately to bigger and better-connected communities. (2) When link probabilities depend on geography, we can compute and compare the centralities of agents in different locations. (3) In models where connections depend on several independent characteristics, we give a formula that determines centralities 'characteristic-by-characteristic'. The basic techniques from these applications, which use the main theorems to reduce questions about random networks to deterministic calculations, extend to many network games.