Published In

Dynamics

Document Type

Article

Publication Date

6-25-2025

Subjects

Metric graphs, Cumulative distribution functions, Kolmogorov–Smirnov, Helmholtz equation

Abstract

In this work, we introduce an edge centrality measure for the Helmholtz equation on metric graphs, a particular flow network, based on spectral edge energy density. This measure identifies influential edges whose removal significantly changes the energy flow on the network, as indicated by statistically significant p-values from the two-sample Kolmogorov–Smirnov test comparing edge energy densities in the original network to those with a single edge removed. We compare the proposed measure with eight vertex centrality measures applied to a line graph representation of each metric graph, as well as with two edge centrality measures applied directly to each metric graph. Both methods are evaluated on two undirected and weighted metric graphs—a power grid network adapted from the IEEE 14-bus system and an approximation of Poland’s road network—both of which are multigraphs. Two experiments evaluate how each measure’s edge ranking impacts the energy flow on the network. The results demonstrate that the proposed measure effectively identifies influential edges in metric graphs that significantly change the energy distribution.

Rights

Copyright: © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/).

DOI

10.3390/dynamics5020016

Persistent Identifier

https://archives.pdx.edu/ds/psu/43947

Publisher

MDPI AG

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