Graph Peeling Semantics

Recently, Graph Cities [1, 2] have been proposed as scalable 3d visual representations of graph edge partitions where each subgraph in the partition is a “fixed point of degree peeling”. In this work, we propose “intuitive” primitives to extract language semantics from the topology of these fixed points aided by provided graph vertex labels. The main approach is to view the collection of data labels as a set system derived from the graph topology and to derive “intuitive” language semantics from a specially derived set system intersection meta-graph. Exploration primitives include a glyph grid map of the distribution of all fixed points in the data set and a textual summary tool. We illustrate our approach with a variety of fixed points subgraphs extracted from “large” datasets that include a patent citation network (16.5 million edges) [3], a movie keywords co-occurrence network derived from the Internet Movie Database (5 million edges), a paper citation network derived from arXiv Computer Science papers (1.5 million edges), and a Parler dataset [4].