Analyzing Network Robustness via Residual Closeness
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914469045600256 |
|---|---|
| author | Golpek, Hande Tuncel Bilici, Mehmet Ali Aytac, Aysun |
| author_facet | Golpek, Hande Tuncel Bilici, Mehmet Ali Aytac, Aysun |
| contents | Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a particular focus on the middle graph representations of certain special graph classes, which provide a richer structural framework for analysis. We derive exact expressions for the closeness values of these middle graphs and determine their residual closeness under vertex failures. By utilizing results obtained from specific graph families, we establish several general bounds for broader graph classes. Furthermore, by exploiting the relationship between the closeness of a graph, its line graphs, and middle graphs, we obtain new results that relate these three structures. In addition, we propose an algorithm for computing closeness in middle graphs and provide a detailed analysis of its performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11267 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Analyzing Network Robustness via Residual Closeness Golpek, Hande Tuncel Bilici, Mehmet Ali Aytac, Aysun Discrete Mathematics Combinatorics 05C69, 05C76, 68R10 Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a particular focus on the middle graph representations of certain special graph classes, which provide a richer structural framework for analysis. We derive exact expressions for the closeness values of these middle graphs and determine their residual closeness under vertex failures. By utilizing results obtained from specific graph families, we establish several general bounds for broader graph classes. Furthermore, by exploiting the relationship between the closeness of a graph, its line graphs, and middle graphs, we obtain new results that relate these three structures. In addition, we propose an algorithm for computing closeness in middle graphs and provide a detailed analysis of its performance. |
| title | Analyzing Network Robustness via Residual Closeness |
| topic | Discrete Mathematics Combinatorics 05C69, 05C76, 68R10 |
| url | https://arxiv.org/abs/2604.11267 |