Combinatorica
An Upper Bound on the Diameter of a Graph from Eigenvalues Associated with its Laplacian
SIAM Journal on Discrete Mathematics
Hypergraphs, quasi-randomness, and conditions for regularity
Journal of Combinatorial Theory Series A
A Dirac-Type Theorem for 3-Uniform Hypergraphs
Combinatorics, Probability and Computing
Loose Hamilton cycles in 3-uniform hypergraphs of high minimum degree
Journal of Combinatorial Theory Series B
Hamiltonian chains in hypergraphs
Journal of Graph Theory
Conductance and convergence of Markov chains-a combinatorial treatment of expanders
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Dirac-type results for loose Hamilton cycles in uniform hypergraphs
Journal of Combinatorial Theory Series B
Loose laplacian spectra of random hypergraphs
Random Structures & Algorithms
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Despite of the extreme success of the spectral graph theory, there are relatively few papers applying spectral analysis to hypergraphs. Chung first introduced Laplacians for regular hypergraphs and showed some useful applications. Other researchers treated hypergraphs as weighted graphs and then studied the Laplacians of the corresponding weighted graphs. In this paper, we aim to unify these very different versions of Laplacians for hypergraphs. We introduce a set of Laplacians for hypergraphs through studying high-ordered random walks on hypergraphs. We prove the eigenvalues of these Laplacians can effectively control the mixing rate of high-ordered random walks, the generalized distances/diameters, and the edge expansions.