Kemeny's constant for a graph with bridges

TL;DR

This paper derives a formula for Kemeny's constant in graphs with bridges, enabling efficient computation and optimization, with potential applications in network analysis and related fields.

Contribution

It introduces a novel formula for Kemeny's constant in graphs with bridges, linking it to subgraph properties for easier computation and analysis.

Findings

The formula simplifies calculating Kemeny's constant for complex graphs.

Optimization problems for graphs with bridges are addressed using the new formula.

The approach offers computational advantages over previous methods.

Abstract

In this paper, we determine a formula for Kemeny's constant for a graph with multiple bridges, in terms of quantities that are inherent to the subgraphs obtained upon removal of all bridges and that can be computed independently. With the formula, we consider several optimization problems for Kemeny's constant for graphs with bridges, and we remark on the computational benefit of this formula for the computation of Kemeny's constant. Finally, we discuss some potential applications.