Random graph models for directed acyclic networks

TL;DR

This paper introduces two random graph models for directed acyclic graphs, analyzing their properties and demonstrating strong agreement with real-world networks like citation networks and neural networks.

Contribution

It proposes novel directed acyclic graph models and provides analytical results that closely match empirical data, improving upon existing models.

Findings

Models accurately predict connection probabilities between vertices.

Theoretical results align well with real-world network data.

Models outperform traditional random graph models in matching real networks.

Abstract

We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the fixed edge number and fixed edge probability variants of traditional undirected random graphs. We calculate a number of properties of these models, including particularly the probability of connection between a given pair of vertices, and compare the results with real-world acyclic network data finding that theory and measurements agree surprisingly well -- far better than the often poor agreement of other random graph models with their corresponding real-world networks.