# Interlacing Results for Hypergraphs

@article{Mulas2021InterlacingRF,
title={Interlacing Results for Hypergraphs},
author={Raffaella Mulas},
journal={Proceedings of Blockchain in Kyoto 2021 (BCK21)},
year={2021}
}
• R. Mulas
• Published 9 June 2021
• Mathematics
• Proceedings of Blockchain in Kyoto 2021 (BCK21)
Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can be inferred from the spectrum, i.e. the multiset of the eigenvalues, of an operator associated to a hypergraph. It is expected that a small perturbation of a hypergraph, such as the removal of a few vertices or edges, does not lead to a major change of the…

## References

SHOWING 1-10 OF 21 REFERENCES

### Spectral Properties of Oriented Hypergraphs

An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of $+1$ or $-1$. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue

### Interlacing for weighted graphs using the normalized Laplacian

The problem of relating the eigenvalues of the normalized Laplacian for a weighted graph G and GH ,f orH a subgraph of G is considered. It is shown that these eigenvalues interlace and that the

### Spectra of hyperstars on public transportation networks

The purpose of this paper is to introduce a model to study structures which are widely present in public transportation networks. We show that, through hypergraphs, one can describe these structures

### Spectral graph theory

• U. Feige
• Mathematics
Zeta and 𝐿-functions in Number Theory and Combinatorics
• 2019
With every graph (or digraph) one can associate several different matrices. We have already seen the vertex-edge incidence matrix, the Laplacian and the adjacency matrix of a graph. Here we shall

### Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian

• Mathematics
• 2019
We offer a new method for proving that the maximal eigenvalue of the normalized graph Laplacian of a graph with $n$ vertices is at least $\frac{n+1}{n-1}$ provided the graph is not complete and that

### Stochastic Dynamics on Hypergraphs and the Spatial Majority Rule Model

• Mathematics
• 2013
This article starts by introducing a new theoretical framework to model spatial systems which is obtained from the framework of interacting particle systems by replacing the traditional graphical

### SIS Epidemic Propagation on Hypergraphs

• Mathematics
Bulletin of mathematical biology
• 2016
The exact master equations of the propagation process are derived for an arbitrary hypergraph given by its incidence matrix, and moment closure approximation and mean-field models are introduced and compared to individual-based stochastic simulations.

### The Quantum Entropy Cone of Hypergraphs

• Computer Science
ArXiv
• 2020
It is shown that, at least up to 4 parties, the hyper graph cone is identical to the stabilizer entropy cone, thus demonstrating that the hypergraph framework is broadly applicable to the study of entanglement entropy.