Highly Dispersed Networks

TL;DR

This paper introduces a novel network growth model via enhanced redirection, resulting in highly-dispersed networks with macrohubs, non-self-averaging behavior, and anomalous degree scaling.

Contribution

It presents a new network growth mechanism that produces networks with multiple macrohubs and unusual scaling properties, expanding understanding of network topology.

Findings

Presence of multiple macrohubs in the network

Networks exhibit non-self-averaging behavior

Degree distribution follows anomalous scaling law

Abstract

We introduce a new class of networks that grow by enhanced redirection. Nodes are introduced sequentially, and each either attaches to a randomly chosen target node with probability 1-r or to the ancestor of the target with probability r, where r an increasing function of the degree of the ancestor. This mechanism leads to highly-dispersed networks with unusual properties: (i) existence of multiple macrohubs---nodes whose degree is a finite fraction of the total number of network nodes N, (ii) lack of self averaging, and (iii) anomalous scaling, in which N_k, the number of nodes of degree k scales as N_k N^{nu-1}/k^{nu}, with 1<nu<2.