Probability of graphs with large spectral gap by multicanonical Monte Carlo

Details Probability of graphs with large spectral gap by multicanonical Monte Carlo Probability of graphs with large spectral gap by multicanonical Monte Carlo

2010-03-04

arxiv.org/abs/1003.1023v1

Physics

Condensed Matter

Statistical Mechanics

3pages 4figures

Scientific paper

Graphs with large spectral gap are important in various fields such as biology, sociology and computer science. In designing such graphs, an important question is how the probability of graphs with large spectral gap behaves. A method based on multicanonical Monte Carlo is introduced to quantify the behavior of this probability, which enables us to calculate extreme tails of the distribution. The proposed method is successfully applied to random 3-regular graphs and large deviation probability is estimated.

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