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Core–satellite graphs : clustering, assortativity and spectral properties

Estrada, Ernesto and Benzi, Michele (2017) Core–satellite graphs : clustering, assortativity and spectral properties. Linear Algebra and its Applications, 517. pp. 30-52. ISSN 0024-3795

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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 analyze their clustering, assortativity, and spectral properties.