Kolmogorov–Smirnov-Based Edge Centrality Measure for Metric Graphs
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 statistic...
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MDPI AG
2025-05-01
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| Series: | Dynamics |
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| Online Access: | https://www.mdpi.com/2673-8716/5/2/16 |
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| author | Christina Durón Hannah Kravitz Moysey Brio |
| author_facet | Christina Durón Hannah Kravitz Moysey Brio |
| author_sort | Christina Durón |
| collection | DOAJ |
| description | 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 <i>p</i>-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. |
| format | Article |
| id | doaj-art-df6f8ebf3d034eb0bc6a69a9e92b6f5e |
| institution | Matheson Library |
| issn | 2673-8716 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Dynamics |
| spelling | doaj-art-df6f8ebf3d034eb0bc6a69a9e92b6f5e2025-06-25T13:43:36ZengMDPI AGDynamics2673-87162025-05-01521610.3390/dynamics5020016Kolmogorov–Smirnov-Based Edge Centrality Measure for Metric GraphsChristina Durón0Hannah Kravitz1Moysey Brio2Natural Science Division, Pepperdine University, Malibu, CA 91301, USAFariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR 97201, USADepartment of Mathematics, University of Arizona, Tucson, AZ 85721, USAIn 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 <i>p</i>-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.https://www.mdpi.com/2673-8716/5/2/16metric graphedge centrality measurecumulative distribution functionsKolmogorov–SmirnovHelmholtz equation |
| spellingShingle | Christina Durón Hannah Kravitz Moysey Brio Kolmogorov–Smirnov-Based Edge Centrality Measure for Metric Graphs Dynamics metric graph edge centrality measure cumulative distribution functions Kolmogorov–Smirnov Helmholtz equation |
| title | Kolmogorov–Smirnov-Based Edge Centrality Measure for Metric Graphs |
| title_full | Kolmogorov–Smirnov-Based Edge Centrality Measure for Metric Graphs |
| title_fullStr | Kolmogorov–Smirnov-Based Edge Centrality Measure for Metric Graphs |
| title_full_unstemmed | Kolmogorov–Smirnov-Based Edge Centrality Measure for Metric Graphs |
| title_short | Kolmogorov–Smirnov-Based Edge Centrality Measure for Metric Graphs |
| title_sort | kolmogorov smirnov based edge centrality measure for metric graphs |
| topic | metric graph edge centrality measure cumulative distribution functions Kolmogorov–Smirnov Helmholtz equation |
| url | https://www.mdpi.com/2673-8716/5/2/16 |
| work_keys_str_mv | AT christinaduron kolmogorovsmirnovbasededgecentralitymeasureformetricgraphs AT hannahkravitz kolmogorovsmirnovbasededgecentralitymeasureformetricgraphs AT moyseybrio kolmogorovsmirnovbasededgecentralitymeasureformetricgraphs |