Finite-size scaling in complex networks

TL;DR

This paper develops a finite-size-scaling theory for complex networks, focusing on the FSS exponent, and confirms conjectured values through numerical simulations for models like Ising, SIS, and contact process.

Contribution

It introduces a finite-size-scaling framework for complex networks and conjectures FSS exponents based on droplet-excitation arguments, validated by simulations.

Findings

FSS exponents are conjectured for key models in complex networks.

Numerical simulations support the validity of the FSS conjectures.

The theory provides a new tool for analyzing finite-size effects in network models.

Abstract

A finite-size-scaling (FSS) theory is proposed for various models in complex networks. In particular, we focus on the FSS exponent, which plays a crucial role in analyzing numerical data for finite-size systems. Based on the droplet-excitation (hyperscaling) argument, we conjecture the values of the FSS exponents for the Ising model, the susceptible-infected-susceptible model, and the contact process, all of which are confirmed reasonably well in numerical simulations.