Self-Reinforced Preferential Attachment

TL;DR

This paper studies a self-reinforced preferential attachment model where new vertices attach based on the cumulative degree history, leading to faster degree growth and new insights into the impact of self-reinforcement on network evolution.

Contribution

It introduces a novel self-reinforced preferential attachment model and analyzes how self-reinforcement accelerates degree growth compared to traditional models.

Findings

Degree growth exponent is strictly larger with self-reinforcement.

Vertices' degrees grow polynomially fast over time.

Self-reinforcement significantly influences network evolution dynamics.

Abstract

We consider a preferential attachment random graph with self-reinforcement. Each time a new vertex comes in, it attaches itself to an old vertex with a probability that is proportional to the sum of the degrees of that old vertex at all prior times. The resulting growing graph is a random tree whose vertices have degrees that grow polynomially fast in time. We compute the growth exponent, show that it is strictly larger than the growth exponent in the absence of self-reinforcement, and develop insight into how the self-reinforcement affects the growth. Proofs are based on a stochastic approximation scheme.