Core-satellite Graphs. Clustering, Assortativity and Spectral Properties

TL;DR

This paper analyzes core-satellite graphs, revealing their clustering, disassortativity, and spectral properties, and introduces generalized versions with extended spectral analysis.

Contribution

It provides a comprehensive spectral characterization of core-satellite graphs and introduces generalized variants, expanding understanding of their structural and spectral features.

Findings

Clustering coefficients diverge with graph size.

Core-satellite graphs are disassortative.

Spectral properties are fully described for adjacency and Laplacian matrices.

Abstract

Core-satellite graphs (sometimes referred to as generalized friendship graphs) are an interesting class of graphs that generalize many well known types of graphs. In this paper we show that two popular clustering measures, the average Watts-Strogatz clustering coefficient and the transitivity index, diverge when the graph size increases. We also show that these graphs are disassortative. In addition, we completely describe the spectrum of the adjacency and Laplacian matrices associated with core-satellite graphs. Finally, we introduce the class of generalized core-satellite graphs, and we analyze the spectral properties of such graphs.