Global information from local observations of the noisy voter model on a graph

TL;DR

This paper demonstrates that observing a single vertex in the noisy voter model can asymptotically distinguish most pairs of finite graphs based on the frequency of repeated observations, revealing new insights into graph identification.

Contribution

It introduces a method to distinguish graphs from local observations of the noisy voter model and proves asymptotic normality of the distinguishing statistic.

Findings

The statistic is asymptotically normal.

Most pairs of finite graphs can be distinguished.

Conjecture: all graphs except stars are distinguishable.

Abstract

We observe the outcome of the discrete time noisy voter model at a single vertex of a graph. We show that certain pairs of graphs can be distinguished by the frequency of repetitions in the sequence of observations. We prove that this statistic is asymptotically normal and that it distinguishes between (asymptotically) almost all pairs of finite graphs. We conjecture that the noisy voter model distinguishes between any two graphs other than stars.