Distances and large deviations in the spatial preferential attachment model

TL;DR

This paper studies the spatial preferential attachment model, revealing that typical distances grow extremely slowly and establishing a large deviation principle for its local structure, with implications for understanding complex networks.

Contribution

It provides new asymptotic results on distances and large deviations in a spatial preferential attachment model, connecting network structure to entropy minimization.

Findings

Distances are at most doubly-logarithmic in size

Large deviation principle for empirical neighborhood structure

Rate function characterized by entropy minimization

Abstract

We investigate two asymptotic properties of a spatial preferential-attachment model introduced by E. Jacob and P. M\"orters (2013). First, in a regime of strong linear reinforcement, we show that typical distances are at most of doubly-logarithmic order. Second, we derive a large deviation principle for the empirical neighbourhood structure and express the rate function as solution to an entropy minimisation problem in the space of stationary marked point processes.