The second eigenvalue of random walks on symmetric random intersection graphs

Authors:
Sotiris Nikoletseas;Christoforos Raptopoulos;Paul G. Spirakis
Affiliations:
Computer Technology Institute, Patras, Greece and University of Patras, Patras, Greece;Computer Technology Institute, Patras, Greece and University of Patras, Patras, Greece;Computer Technology Institute, Patras, Greece and University of Patras, Patras, Greece
Venue:
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
Year:
2007

Citing 9
Cited 2

Approximate counting, uniform generation and rapidly mixing Markov chains

Information and Computation
Algorithms for random generation and counting: a Markov chain approach

Algorithms for random generation and counting: a Markov chain approach
Approximating layout problems on random geometric graphs

Journal of Algorithms
Short Vertex Disjoint Paths and Multiconnectivity in Random Graphs: Reliable Network Computing

ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
A Random Graph Model for Optical Networks of Sensors

IEEE Transactions on Mobile Computing
On Random Intersection Graphs: The Subgraph Problem

Combinatorics, Probability and Computing
The vertex degree distribution of random intersection graphs

Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I
On the existence of hamiltonian cycles in random intersection graphs

ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Simple and efficient greedy algorithms for hamilton cycles in random intersection graphs

ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation

Expander properties and the cover time of random intersection graphs

Theoretical Computer Science
Expander properties and the cover time of random intersection graphs

MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

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