Stochastic dynamical model of a growing network based on self-exciting point process

TL;DR

This paper verifies the preferential attachment model in citation networks, revealing superlinear dynamics and correlations in citation processes, and introduces a stochastic growth model that aligns well with empirical data.

Contribution

The study demonstrates superlinear preferential attachment in citation networks and develops a stochastic model that accurately reproduces observed citation distributions.

Findings

Citation dynamics follow superlinear preferential attachment with exponent 1.25-1.3.

Citation process exhibits correlations, not memoryless Markovian behavior.

The proposed stochastic model matches empirical citation distributions.

Abstract

We perform experimental verification of the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose citation network of Physics papers and traced citation history of 40,195 papers published in one year. Contrary to common belief, we found that citation dynamics of the individual papers follows the \emph{superlinear} preferential attachment, with the exponent $\alpha= 1.25-1.3$. Moreover, we showed that the citation process cannot be described as a memoryless Markov chain since there is substantial correlation between the present and recent citation rates of a paper. Basing on our findings we constructed a stochastic growth model of the citation network, performed numerical simulations based on this model and achieved an excellent agreement with the measured citation distributions.