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Isoperimetric Numbers of Randomly Perturbed Intersection Graphs

Department of Computer and Information Sciences, Faculty of Engineering and Environment, Northumbria University, Newcastle NE1 8ST, UK
Symmetry 2019, 11(4), 452; https://doi.org/10.3390/sym11040452
Received: 2 February 2019 / Revised: 26 March 2019 / Accepted: 27 March 2019 / Published: 1 April 2019
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
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Abstract

Social networks describe social interactions between people, which are often modeled by intersection graphs. In this paper, we propose an intersection graph model that is induced by adding a sparse random bipartite graph to a given bipartite graph. Under some mild conditions, we show that the vertex–isoperimetric number and the edge–isoperimetric number of the randomly perturbed intersection graph on n vertices are Ω ( 1 / ln n ) asymptomatically almost surely. Numerical simulations for small graphs extracted from two real-world social networks, namely, the board interlocking network and the scientific collaboration network, were performed. It was revealed that the effect of increasing isoperimetric numbers (i.e., expansion properties) on randomly perturbed intersection graphs is presumably independent of the order of the network. View Full-Text
Keywords: isoperimetric number; random graph; intersection graph; social network isoperimetric number; random graph; intersection graph; social network
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Shang, Y. Isoperimetric Numbers of Randomly Perturbed Intersection Graphs. Symmetry 2019, 11, 452.

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