Bias in generation of random graphs

TL;DR

This paper investigates the bias introduced in the efficient generation of random graphs using the configuration model, revealing persistent biases that affect properties like graph diameter, especially in scale-free networks with broad degree distributions.

Contribution

It explicitly calculates the bias in the efficient graph generation process and demonstrates its persistence regardless of system size, highlighting challenges in generating certain scale-free graphs.

Findings

Bias does not vanish as system size grows.

Efficient generation methods introduce systematic biases.

Bias impacts measurements like graph diameter in scale-free graphs.

Abstract

We study the statistical properties of the generation of random graphs according the configuration model, where one assigns randomly degrees to nodes. This model is often used, e.g., for the scale-free degree distribution ~d^gamma. For the efficient variant, where non-feasible edges are rejected and the construction of a graph continues, there exists a bias, which we calculate explicitly for a small sample ensemble. We find that this bias does not disappear with growing system size. This becomes also visible, e.g., for scale-free graphs when measuring quantities like the graph diameter. Hence, the efficient generation of general scale-free graphs with a very broad distribution (gamma <2) remains an open problem.