Simple model of fractal networks formed by self-organized critical dynamics

TL;DR

This paper introduces a simple dynamical model demonstrating how self-organized criticality can lead to the formation of fractal networks, with power-law distributions and fractal properties emerging naturally.

Contribution

The model shows that SOC dynamics can produce fractal networks with power-law cluster and collapse size distributions, linking criticality to fractal network formation.

Findings

Cluster and collapse sizes follow power-law distributions.

Networks exhibit fractal structures due to SOC dynamics.

Criticality aligns with mean-field universality class.

Abstract

In this paper, a simple dynamical model in which fractal networks are formed by self-organized critical (SOC) dynamics is proposed; the proposed model consists of growth and collapse processes. It has been shown that SOC dynamics are realized by the combined processes in the model. Thus, the distributions of the cluster size and collapse size follow a power-law function in the stationary state. Moreover, through SOC dynamics, the networks become fractal in nature. The criticality of SOC dynamics is the same as the universality class of mean-field theory. The model explains the possibility that the fractal nature in complex networks emerges by SOC dynamics in a manner similar to the case with fractal objects embedded in a Euclidean space.