The Census-Stub Graph Invariant Descriptor

TL;DR

The paper introduces Census-Stub, a novel invariant graph descriptor focusing on stubs, which significantly improves graph distinction capabilities without high computational costs, and presents new visualization methods for graph analysis.

Contribution

It presents the BFS-Census algorithm and Census-Stub descriptor, enhancing graph invariance and discrimination power while maintaining efficiency, along with innovative visualization techniques.

Findings

Census-Stub outperforms existing descriptors in graph isomorphism tests.

The method maintains low storage and computational costs.

New visualizations effectively represent graph topology changes.

Abstract

An invariant descriptor captures meaningful structural features of networks, useful where traditional visualizations, like node-link views, face challenges like the hairball phenomenon (inscrutable overlap of points and lines). Designing invariant descriptors involves balancing abstraction and information retention, as richer data summaries demand more storage and computational resources. Building on prior work, chiefly the BMatrix -- a matrix descriptor visualized as the invariant network portrait heatmap -- we introduce BFS-Census, a new algorithm computing our Census data structures: Census-Node, Census-Edge, and Census-Stub. Our experiments show Census-Stub, which focuses on stubs (half-edges), has orders of magnitude greater discerning power (ability to tell non-isomorphic graphs apart) than any other descriptor in this study, without a difficult trade-off: the substantial increase in resolution does not come at a commensurate cost in storage space or computation power. We also present new visualizations -- our Hop-Census polylines and Census-Census trajectories -- and evaluate them using real-world graphs, including a sensitivity analysis that shows graph topology change maps to visual Census change.