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.

翻译：网络可能是高度复杂的系统，包含大量相互连接的组件和交互。粒计算通过将网络分解为更小、更易管理的组件（即粒）来应对这种复杂性。本文提出一种基于度量的粒计算技术来研究网络。该技术可应用于网络分析，其中粒可表示节点或边的子集，且其交互可在不同粒度层次上进行研究。我们将网络建模为信息系统，并利用度量表示探究其粒结构。我们证明了粗糙集理论中的约简概念与网络中的分辨集概念是等价的。基于这一等价关系，我们提出了一种计算这些网络所有最小分辨集的新方法。