In this paper we examine spectral properties of random intersection graphs when the number of vertices is equal to the number of labels. We call this class symmetric random intersection graphs. We examine symmetric random intersection graphs when the probability that a vertex selects a label is close to the connectivity threshold τc. In particular, we examine the size of the second eigenvalue of the transition matrix corresponding to the Markov Chain that describes a random walk on an instance of the symmetric random intersection graph Gn,n,p. We show that with high probability the second eigenvalue is upper bounded by some constant ζ < 1. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Nikoletseas, S., Raptopoulos, C., & Spirakis, P. G. (2007). The second eigenvalue of random walks on symmetric random intersection graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4728 LNCS, pp. 236–246). Springer Verlag. https://doi.org/10.1007/978-3-540-75414-5_15
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