Preferential compactness of networks

TL;DR

This paper introduces a model of evolving networks where new nodes preferentially connect to central parts, resulting in compact structures that exhibit complex architectures in finite cases but tend to less connected forms infinitely, linking self-optimization and self-organization.

Contribution

It presents an analytical solution for preferential compactness in tree-like networks, connecting network growth mechanisms to complex architecture emergence.

Findings

Finite networks are complex and compact.

Infinite networks tend to less connected structures.

Analytical solutions for tree-like networks are provided.

Abstract

We introduce evolving networks where new vertices preferentially connect to the more central parts of a network. This makes such networks compact. Finite networks grown under the preferential compactness mechanism have complex architectures, but infinite ones tend towards the opposite, having rapidly decreasing distributions of connections. We present an analytical solution of the problem for tree-like networks. Our approach links a collective self-optimization mechanism of the emergence of complex network architectures to self-organization mechanisms.