The Second Eigenvalue of Random Walks On Symmetric Random Intersection Graphs

  • Sotiris Nikoletseas
  • Christoforos Raptopoulos
  • Paul G. Spirakis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4728)


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 τ c . 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 G n, n, p. We show that with high probability the second eigenvalue is upper bounded by some constant ζ< 1.


Random Walk Random Graph Hamilton Cycle Transition Probability Matrix Steady State Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Sotiris Nikoletseas
    • 1
    • 2
  • Christoforos Raptopoulos
    • 1
    • 2
  • Paul G. Spirakis
    • 1
    • 2
  1. 1.Computer Technology Institute, P.O. Box 1122, 26110 PatrasGreece
  2. 2.University of Patras, 26500 PatrasGreece

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