On Generating Random Graphs Based on Fuzzy Proximity Relationships between Vertices

Uncertain graphs are getting more and more important. They allow to tackle fuzzy situations in numerous frameworks. This paper investigates the issue of generating random graphs based on uncertain proximity relationships between vertices and the goal is to construct the most likely graph. The Constraint Programming paradigm was used to provide a systematic way to release uncertain graphs while maximizing and minimizing the paths that separate certain vertex pairs. The proposed approach allowed to generate uncertain graphs at a reasonable time. This is confirmed by experimental results obtained from a series of tests on several instances. Our solution lays the basis for further real world applications in different fields, such as analytical chemistry, telecommunication networks, and civil engineering.