Sharp Bounds for the Largest Eigenvalue

TL;DR: In this paper, the spectral properties of the normalized Laplacian defined for chemical hypergraphs are discussed and two Courant nodal domain theorems are established; new quantities that bound the eigenvalues are introduced.

TL;DR: In this paper, the authors generalized the vertex Laplacian and the hyperedge Laplace operator for oriented hypergraphs, for all polylogarithm Ω(p) ≥ 1.

TL;DR: The spectral theory of the normalized Laplacian for chemical hypergraphs is further investigated in this paper , where it is shown that the spectrum for classical hypergraph with respect to the normalized lplacians coincides with the spectrum of bipartite chemical hyperGraphs.

TL;DR: It is shown that the second largest eigenvalue of the generalized normalized Laplacian is bounded both above and below by the generalized Cheeger constant, and the corresponding eigenfunctions can be used to approximate the Cheeger cut.

TL;DR: This work generalizes the master stability approach to hypergraphs and provides a blueprint for how to generalize dynamical structures and results from graphs tohypergraphs.

TL;DR: In this article, the normalized combinatorial Laplace operator for graphs was generalized to hypergraphs, and two Laplace operators for hypergraph hypergraph for chemical reaction networks were defined.

TL;DR: In this paper, the spectrum of the normalized Laplace operator of a connected graph is studied and the smallest eigenvalue can be controlled by the Cheeger constant, and a dual construction that controls the largest eigen value is established.

TL;DR: In this paper, the adjacency and Laplacian eigenvalues of an oriented hypergraph are studied, and the spectral radius and eigenvalue bounds for both the vertex-edge incidence matrix and the matrix matrix of the oriented signed graph are derived.