Corona graphs as a model of small-world networks

TL;DR

This paper introduces recursive corona graphs as a new model for small-world networks, providing explicit analytical results for key network properties that resemble real-world networks.

Contribution

The paper presents a novel recursive corona graph model and derives explicit formulas for its structural and spectral properties, advancing understanding of small-world network modeling.

Findings

Explicit formulas for degree distribution, clustering coefficient, and path length.

Spectral analysis of adjacency and Laplacian matrices.

Model's properties closely match those of real-world networks.

Abstract

We introduce recursive corona graphs as a model of small-world networks. We investigate analytically the critical characteristics of the model, including order and size, degree distribution, average path length, clustering coefficient, and the number of spanning trees, as well as Kirchhoff index. Furthermore, we study the spectra for the adjacency matrix and the Laplacian matrix for the model. We obtain explicit results for all the quantities of the recursive corona graphs, which are similar to those observed in real-life networks.