Self-Coordinated Corona Graphs: a model for complex networks

TL;DR

This paper introduces Self-Coordinated Corona Graphs (SCCG), a deterministic network model inspired by real-world networks with constant or shrinking diameter and power-law degree distribution, emphasizing self-organization.

Contribution

The paper proposes a novel SCCG model based on corona products and self-coordination, analytically proving its power-law exponent and constant diameter, and compares it with existing models.

Findings

SCCG exhibits a power-law degree distribution with an exponent around 2.

The diameter of SCCG remains constant for certain motifs.

SCCG shares properties with real-world complex networks.

Abstract

Recently, real world networks having constant/shrinking diameter along with power-law degree distribution are observed and investigated in literature. Taking an inspiration from these findings, we propose a deterministic complex network model, which we call Self-Coordinated Corona Graphs (SCCG), based on the corona product of graphs. As it has also been established that self coordination/organization of nodes gives rise to emergence of power law in degree distributions of several real networks, the networks in the proposed model are generated by the virtue of self coordination of nodes in corona graphs. Alike real networks, the SCCG inherit motifs which act as the seed graphs for the generation of SCCG. We also analytically prove that the power law exponent of SCCG is approximately $2$ and the diameter of SCCG produced by a class of motifs is constant. Finally, we compare different properties of the proposed model with that of the BA and Pseudofractal scale-free models for complex networks.