Synchronous and Asynchronous Recursive Random Scale-Free Nets

TL;DR

This paper compares scale-free recursive networks built via synchronous deterministic updates and asynchronous random updates, revealing that observed differences in degree exponents are due to biases in node update sequences.

Contribution

It clarifies the cause of discrepancies in degree exponents between synchronous and asynchronous recursive nets, attributing them to update bias effects.

Findings

Degree exponents differ significantly between the two updating methods.

Bias in node selection during asynchronous updates explains the observed discrepancies.

Synchronous and asynchronous recursive nets are fundamentally different in their degree distributions.

Abstract

We investigate the differences between scale-free recursive nets constructed by a synchronous, deterministic updating rule (e.g., Apollonian nets), versus an asynchronous, random sequential updating rule (e.g., random Apollonian nets). We show that the dramatic discrepancies observed recently for the degree exponent in these two cases result from a biased choice of the units to be updated sequentially in the asynchronous version.