Isoperimetric Numbers of Randomly Perturbed Intersection Graphs
Department of Computer and Information Sciences, Faculty of Engineering and Environment, Northumbria University, Newcastle NE1 8ST, UK
Received: 2 February 2019 / Revised: 26 March 2019 / Accepted: 27 March 2019 / Published: 1 April 2019
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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
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.
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MDPI and ACS Style
Shang, Y. Isoperimetric Numbers of Randomly Perturbed Intersection Graphs. Symmetry 2019, 11, 452.
Shang Y. Isoperimetric Numbers of Randomly Perturbed Intersection Graphs. Symmetry. 2019; 11(4):452.
Shang, Yilun. 2019. "Isoperimetric Numbers of Randomly Perturbed Intersection Graphs." Symmetry 11, no. 4: 452.
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