The Census-Stub Graph Invariant Descriptor

Area of Science:

• Graph theory
• Network analysis
• Data visualization

Background:

• Traditional network visualizations like node-link diagrams suffer from the 'hairball phenomenon,' obscuring network structure.
• Invariant descriptors offer an alternative by summarizing network features, but designing them requires balancing data abstraction with information retention.
• Previous work includes the BMatrix descriptor, visualized as a 'network portrait' heatmap.

Purpose of the Study:

• Introduce BFS-Census, a novel algorithm for computing network invariant descriptors.
• Develop new data structures: Census-Node, Census-Edge, and Census-Stub.
• Evaluate the performance and visualization capabilities of these new descriptors.

Main Methods:

• Developed the BFS-Census algorithm to compute Census data structures.
• Focused on the Census-Stub descriptor, which analyzes network 'stubs' (half-edges).
• Created new visualizations: Hop-Census polylines and Census-Census trajectories.

Main Results:

• Census-Stub demonstrated orders of magnitude greater discerning power compared to other descriptors in the study.
• This enhanced resolution was achieved without a significant increase in storage space or computational cost.
• New visualizations effectively mapped graph topology changes to visual changes in Census representations.

Conclusions:

• BFS-Census, particularly the Census-Stub descriptor, provides a powerful and efficient method for network analysis.
• The developed visualizations offer intuitive ways to explore network structures and their changes.
• This approach effectively addresses the limitations of traditional network visualization techniques.