Core-satellite Graphs. Clustering, Assortativity and Spectral Properties

2015/10/08 by Ernesto Estrada, Michele Benzi, Estrada, Ernesto +1 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI) #cs.SI #math.CO #physics.soc-ph

paper · pdf · doi:10.48550/arxiv.1510.07954

15 pages, 6 figures

arxiv created 2015/10/08 · arxiv updated 2015/11/27

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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