Core-satellite Graphs. Clustering, Assortativity and Spectral Properties

Ernesto Estrada; Michele Benzi

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arXiv · 1510.07954

Core-satellite Graphs. Clustering, Assortativity and Spectral Properties

Ernesto Estrada·Michele Benzi

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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.

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Ernesto Estrada, Michele Benzi. 2015-10-08. Core-satellite Graphs. Clustering, Assortativity and Spectral Properties. https://arxiv.org/abs/1510.07954

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