Visual Analysis of Vertex-Disjoint Path Connectivity in Networks

Abstract

The visualization of large graphs in interactive applications, specifically on small devices, can make harder to understand and analyze the displayed information. We show as simple topological properties of the graph can provide an efficient automatic computation of features which improves the "readibility" of a large graph by a proper selection of the displayed information. The connectivity (existence of a path) is a very intuitive structural property of a network; in this paper we propose an approach to the visualization of a network based on connectivity and related concepts as effective tools for visual analysis. In particular, given a root vertex r and a target vertex t, it is possible to check at a glance if there are some dominators, i.e., mandatory vertices that are on every path from r to t. Furthermore, using a recent graph algorithm from Georgiadis and Tarjan [19], [20], by selecting a target vertex it is possible to see two distinct paths from r to t: the paths are vertex-disjoints if there are no dominators from r to t, otherwise the paths have only the dominators in common. We conclude by presenting, as a relevant case study that motivated our work, as this approach improves a personalized eLearning application. In a framework, presented in [27], for dynamic configuration of paths of learning activities for both individual and group education, we can add visual analysis capabilities for both the final user/learner, and for the administrator of a repository.