Graph Reduction in a Path Information-Based Rough Directed Graph Model

Rough graphs have been designed by investigating graphs in the framework of rough sets and can be used to represent networks with uncertain information. However, the existing research on rough graphs has not considered graph characteristics, such as path information. To address this shortcoming, this paper considers the transitive closure and minimum equivalent graph, which keep the path information of a directed graph unchanged. Namely, using the minimum equivalent graph and the transitive closure to approximate a directed graph, a path information-based rough directed graph (PIRDG) model is constructed. In addition, the current studies on granular structure reduction in graphs have been mostly focused on vertex reduction, which cannot make full use of structural information contained in graphs. To address this limitation, the paper introduces three graph reducts by treating each directed graph as a PIRDG, studies the relationship between them, and proposes a method to determine an optimal graph reduct. The proposed PIRDG model is verified under the conditions of rumor propagation and communication network reduction, its practicability in decision making is demonstrated, and the result shows that this model is more efficient than other rough graph models in some fields such as information dissemination.