Analytic connectivity of $k$-uniform hypergraphs

TL;DR

This paper investigates the analytic connectivity of k-uniform hypergraphs, providing exact calculations for complete hypergraphs and establishing bounds relating it to various graph invariants.

Contribution

It introduces bounds on the analytic connectivity of k-uniform hypergraphs and computes it explicitly for complete hypergraphs.

Findings

Exact analytic connectivity for complete k-graphs

Bounds relating analytic connectivity to degree, vertex connectivity, diameter, and isoperimetric number

Theoretical relationships between hypergraph invariants and analytic connectivity

Abstract

In this paper, we study the analytic connectivity of a $k$-uniform hypergraph $H$, denoted by $\alpha(H)$. In addition to computing the analytic connectivity of a complete $k$-graph, we present several bounds on analytic connectivity that relate it with other graph invariants, such as degree, vertex connectivity, diameter, and isoperimetric number.