Random acyclic networks

TL;DR

This paper introduces a new random graph model for directed acyclic graphs, providing analytical solutions and a simulation algorithm, and demonstrates its effectiveness by fitting a citation network of physics papers.

Contribution

It presents a novel random acyclic network model with analytical solutions and a fast simulation algorithm, validated against real-world citation data.

Findings

Model accurately predicts connection probabilities.

Model matches component size distributions.

Good agreement with real citation network data.

Abstract

Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the model's properties, including connection probabilities and component sizes, as well as a fast algorithm for simulating the model on a computer. We compare the predictions of the model to a real-world network of citations between physics papers and find surprisingly good agreement, suggesting that the structure of the real network may be quite well described by the random graph.