Some granular structures for weighted digraphs

Graphs are non-Euclidean data structures used to model interaction relationships between abstract objects. When additional structures, such as graph orientation, weighted vertices, or weight functions on edges, are imposed on the graph, additional graph properties can be applied to discover hidden patterns within the structure of the graph. In this paper, we discuss possible granular structures for graphs, with a focus on granular structure for edge-weighted digraphs derived from pairwise comparison problems. These structures have been applied in various fields such as recommender systems, graph databases, and social network analysis.