Random Networks Tossing Biased Coins

TL;DR

This paper introduces a simple, efficient method to generate directed random graphs with scale-free outdegree and compact indegree, useful for statistical mechanics studies of complex networks.

Contribution

It presents a new biased coin-tossing algorithm for creating directed graphs with specific degree distributions, with analytical insights into key observables.

Findings

Algorithm works well for graphs of size n ~ 100

Many observables can be derived analytically

Improves upon previous models for similar graphs

Abstract

In statistical mechanical investigations on complex networks, it is useful to employ random graphs ensembles as null models, to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to generate an ensemble of random directed graphs with, asymptotically, scale-free outdegree and compact indegree. Entries in each row of the adjacency matrix are set to be zero or one according to the toss of a biased coin, with a chosen probability distribution for the biases. This defines a quick and simple algorithm, which yields good results already for graphs of size n ~ 100. Perhaps more importantly, many of the relevant observables are accessible analytically, improving upon previous estimates for similar graphs.