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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2503.02901 |
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| _version_ | 1866909525271904256 |
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| author | Arshad, Hibba Javaid, Imran |
| author_facet | Arshad, Hibba Javaid, Imran |
| contents | Networks can be highly complex systems with numerous interconnected components and interactions. Granular computing offers a framework to manage this complexity by decomposing networks into smaller, more manageable components, or granules. In this article, we introduce metric-based granular computing technique to study networks. This technique can be applied to the analysis of networks where granules can represent subsets of nodes or edges and their interactions can be studied at different levels of granularity. We model the network as an information system and investigate its granular structures using metric representation. We establish that the concepts of reducts in rough set theory and resolving sets in networks are equivalent. Through this equivalence, we present a novel approach for computing all the minimal resolving sets of these networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02901 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Metric-Based Granular Computing in Networks Arshad, Hibba Javaid, Imran Social and Information Networks Discrete Mathematics 05C12, 05A18, 05C62 Networks can be highly complex systems with numerous interconnected components and interactions. Granular computing offers a framework to manage this complexity by decomposing networks into smaller, more manageable components, or granules. In this article, we introduce metric-based granular computing technique to study networks. This technique can be applied to the analysis of networks where granules can represent subsets of nodes or edges and their interactions can be studied at different levels of granularity. We model the network as an information system and investigate its granular structures using metric representation. We establish that the concepts of reducts in rough set theory and resolving sets in networks are equivalent. Through this equivalence, we present a novel approach for computing all the minimal resolving sets of these networks. |
| title | Metric-Based Granular Computing in Networks |
| topic | Social and Information Networks Discrete Mathematics 05C12, 05A18, 05C62 |
| url | https://arxiv.org/abs/2503.02901 |