Organization of complex networks without multiple connections

TL;DR

This paper uncovers a new structural feature in equilibrium complex networks without multiple connections, revealing a core of highly interconnected vertices whose size scales with the network, and revises previous estimates of connection distribution cut-offs.

Contribution

It identifies a core structure in such networks and provides new scaling laws and distribution cut-off estimates, advancing understanding of network topology.

Findings

Networks contain a highly interconnected core when connections are abundant.

Core size scales between const N^{1/2} and const N^{2/3}.

Distribution cut-off position differs from earlier estimates.

Abstract

We find a new structural feature of equilibrium complex random networks without multiple and self-connections. We show that if the number of connections is sufficiently high, these networks contain a core of highly interconnected vertices. The number of vertices in this core varies in the range between $const N^{1/2}$ and $const N^{2/3}$, where $N$ is the number of vertices in a network. At the birth point of the core, we obtain the size-dependent cut-off of the distribution of the number of connections and find that its position differs from earlier estimates.