Eigenvalues of Non-backtracking Walks in a Cycle with Random Loops
نویسنده
چکیده
In this paper we take a very special model of a random non-regular graph and study its non-backtracking spectrum. We study graphs consisting of a cycle with some random loops added; the graphs are not regular and their non-backtracking spectrum does not seem to be confined to some one-dimensional set in the complex plane. The nonbacktracking spectrum is required in some applications, and has no straightforward connection to the usual adjacency matrix spectrum for general graphs, unlike the situation for regular graphs. Experimentally, the random graphs’ spectrum appears similar in shape to its deterministic counterpart, but differs because the eigenvalues are visibly clustered, especially with a mysterious gap around Re(λ) = 1. ∗Department of Computer Science, Princeton University, Princeton, NJ 08540 [email protected]
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