Estrada index and subgraph centrality of hypergraphs via tensors

TL;DR

This paper explores the Estrada index and subgraph centrality of uniform hypergraphs using tensor representations, providing bounds and expressions that connect hypergraph properties to graph parameters.

Contribution

It introduces methods to analyze hypergraph centrality measures via tensors, extending concepts from graphs to hypergraphs and establishing new bounds and formulas.

Findings

Derived bounds for the Estrada index of hypergraphs

Expressed subgraph centrality in terms of associated digraph parameters

Specialized results for 2-uniform hypergraphs (graphs)

Abstract

Uniform hypergraphs have a natural one-to-one correspondence to tensors. In this paper, we investigate the Estrada index and subgraph centrality of an $m$-uniform hypergraph $\mathcal{H}$ via the adjacency tensor. We establish some bounds for the Estrada index and give expressions of the subgraph centrality in terms of graph parameters of the multi-digraphs associated with $\mathcal{H}$. When $\mathcal{H}$ is $2$-uniform, the above Estrada index and subgraph centrality are the Estrada index and subgraph centrality of a graph.