In this paper, we investigate the theory of rough set to study graphs using the concept of orbits. Rough sets are based on a clustering criterion and we use the idea of similarity of vertices under automorphism as a criterion. We introduce indiscernibility relation in terms of orbits and prove necessary and sufficient conditions under which the indiscernibility partitions remain the same when associated with different attribute sets. We show that automorphisms of the graph $\mathcal{G}$ preserve the indiscernibility partitions. Further, we prove that for any graph $\mathcal{G}$ with $k$ orbits, any reduct $\mathcal{R}$ consists of one element from $k-1$ orbits of the graph. We also study the rough membership functions for paths, cycles, complete and complete bipartite graphs. Moreover, we introduce essential sets and discernibility matrices induced by orbits of graphs and study their relationship. We also prove that every essential set consists of union of any two orbits of the graph.

Networks are commonly represented as graphs, where vertices denote entities and edges capture relationships based on shared attributes. Granulation of a network is important for the structural analysis and understanding of its underlying patterns. In this paper, we introduce a distance-based granular computing framework for analyzing networks modeled by intersection graphs. We define these networks as information systems and investigate their granular structures using a distance-based representation. Based on the concepts of indiscernibility between two vertices using the distance from a set, we study indiscernibility partitions on the vertex set. Using the concept of discernibility between vertices, we define the distance-based discernibility matrix and explore its properties. We identify all minimal resolving sets using the discernibility matrix. Furthermore, using the proposed method, we study a transportation network for urban traffic planning.