850 research outputs found
Spectral Properties of Oriented Hypergraphs
An oriented hypergraph is a hypergraph where each vertex-edge incidence is
given a label of or . The adjacency and Laplacian eigenvalues of an
oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and
Laplacian matrices of an oriented hypergraph which depend on structural
parameters of the oriented hypergraph are found. An oriented hypergraph and its
incidence dual are shown to have the same nonzero Laplacian eigenvalues. A
family of oriented hypergraphs with uniformally labeled incidences is also
studied. This family provides a hypergraphic generalization of the signless
Laplacian of a graph and also suggests a natural way to define the adjacency
and Laplacian matrices of a hypergraph. Some results presented generalize both
graph and signed graph results to a hypergraphic setting.Comment: For the published version of the article see
http://repository.uwyo.edu/ela/vol27/iss1/24
A Self-Advocate’s Perspective on the COVID-19 Pandemic
This article summarizes the experience of a self-advocate from Idaho during the COVID pandemic. This article addresses issues of social isolation, mental health, and social supports
Spectral Properties of Complex Unit Gain Graphs
A complex unit gain graph is a graph where each orientation of an edge is
given a complex unit, which is the inverse of the complex unit assigned to the
opposite orientation. We extend some fundamental concepts from spectral graph
theory to complex unit gain graphs. We define the adjacency, incidence and
Laplacian matrices, and study each of them. The main results of the paper are
eigenvalue bounds for the adjacency and Laplacian matrices.Comment: 13 pages, 1 figure, to appear in Linear Algebra App
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