Adjacency Spectra of Random and Uniform Hypergraphs

Joshua Cooper

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arXiv · 1507.07118

Adjacency Spectra of Random and Uniform Hypergraphs

Joshua Cooper

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Abstract

We present progress on the problem of asymptotically describing the adjacency eigenvalues of random and complete uniform hypergraphs. There is a natural conjecture arising from analogy with random matrix theory that connects these spectra to that of the all-ones hypermatrix. Several of the ingredients along a possible path to this conjecture are established, and may be of independent interest in spectral hypergraph/hypermatrix theory. In particular, we provide a bound on the spectral radius of the symmetric Bernoulli hyperensemble, and show that the spectrum of the complete $k$-uniform hypergraph for $k=2,3$ is close to that of an appropriately scaled all-ones hypermatrix.

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Joshua Cooper. 2015-07-25. Adjacency Spectra of Random and Uniform Hypergraphs. https://arxiv.org/abs/1507.07118

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