Title: Driving Interactive Graph Exploration Using 0-Dimensional Persistent Homology Features,
Abstract: Graphs are commonly used to encode relationships among entities, yet, their
abstractness makes them incredibly difficult to analyze. Node-link diagrams are
a popular method for drawing graphs. Classical techniques for the node-link
diagrams include various layout methods that rely on derived information to
position points, which often lack interactive exploration functionalities; and
force-directed layouts, which ignore global structures of the graph. This paper
addresses the graph drawing challenge by leveraging topological features of a
graph as derived information for interactive graph drawing. We first discuss
extracting topological features from a graph using persistent homology. We then
introduce an interactive persistence barcodes to study the substructures of a
force-directed graph layout; in particular, we add contracting and repulsing
forces guided by the 0-dimensional persistent homology features. Finally, we
demonstrate the utility of our approach across three datasets.