Change point detection in Network models: Preferential attachment and long range dependence

TL;DR

This paper investigates change points in preferential attachment network models, showing how structural properties are affected, and proposes a consistent estimator for detecting such change points, highlighting long-range dependence effects.

Contribution

It provides asymptotic analysis of change points in preferential attachment networks and introduces a novel estimator accounting for non-ergodic network evolution.

Findings

Change points affect degree distribution but not the degree exponent.

The proposed estimator is consistent for detecting change points.

Long-range dependence influences network evolution and change point detection.

Abstract

Inspired by empirical data on real world complex networks, the last few years have seen an explosion in proposed generative models to understand and explain observed properties of real world networks, including power law degree distribution and "small world" distance scaling. In this context, a natural question is the phenomenon of {\it change point}, understanding how abrupt changes in parameters driving the network model change structural properties of the network. We study this phenomenon in one popular class of dynamically evolving networks: preferential attachment models. We derive asymptotic properties of various functionals of the network including the degree distribution as well as maximal degree asymptotics, in essence showing that the change point does effect the degree distribution but does {\bf not} change the degree exponent. This provides further evidence for long range dependence and sensitive dependence of the evolution of the process on the initial evolution of the process in such self-reinforced systems. We then propose an estimator for the change point and prove consistency properties of this estimator. The methodology developed highlights the effect of the non-ergodic nature of the evolution of the network on classical change point estimators.