Traversal-Based Weighting vs. Structural Weighting

 

🧠 1. Traversal-Based Weighting vs. Structural Weighting

Structural Weighting

• Based on static graph topology: node degrees, edge types, and schema annotations.

• Common metrics:

  • In-degree / Out-degree

  • Edge weights

  • Required vs. optional relationships

This is deterministic and reflects the schema design, not runtime behavior.

Traversal-Based Weighting

• Based on how often a node is reached across multiple BFS runs.

• Sensitive to:

  • Graph connectivity

  • Edge directionality

  • BFS root selection

  • Cycles and shared paths

This reflects runtime influence—how central or reachable a node is from others.

📘 Reference: discusses how BFS and DFS reveal different structural roles depending on traversal strategy.

🔄 2. Why Per-Root BFS Causes Oscillation

Each BFS run from a different root:

• Re-triggers edges unless globally marked

• Bumps priority of nodes reachable from that root

• Causes accumulated scores for shared nodes

This leads to:

• Stable top nodes (like ArtistCredit) that are reachable from many roots

• Oscillating middle nodes whose reachability varies by root

• Low-score leaf nodes only reachable from a few places

📘 Reference: explains how traversal order and reachability affect node influence.

🧭 3. Centrality Measures in Graph Theory

You're intuitively touching on centrality, a key concept in network science:

Centrality Type	Meaning	Relevance to Your Graph
Degree Centrality	# of edges connected to a node	Static schema weight
Betweenness	# of shortest paths passing through a node	Traversal frequency
Closeness	Avg distance to all other nodes	BFS depth sensitivity
Eigenvector	Influence based on neighbors' importance	Recursive priority bump

📘 Reference: introduces dynamic centrality in time-varying graphs, which parallels your per-root BFS accumulation.

🧪 4. ETL Prioritization via Graph Traversal

Your BFS-based priority map is a form of dependency-aware ETL scheduling:

• Nodes with high traversal scores are upstream dependencies

• Nodes with low scores are leaf entities or isolated types

• You can use this to:

  • Order inserts to avoid FK violations

  • Batch entities by dependency depth

  • Parallelize ETL phases safely

📘 Reference: explores how traversal patterns can optimize query planning—similar to ETL orchestration.

🧰 5. Practical Enhancements You Could Explore

Here are some advanced ideas to push your model further:

• Weighted BFS: Use edge weights to prioritize traversal paths

• DAG Layering: Assign levels to nodes based on topological depth

• Traversal Heatmaps: Visualize node visit frequency across BFS runs

• Hybrid Scoring: Combine static schema weights with traversal counts

📘 Reference: discusses BFS/DFS edge classification and layering—perfect for ETL phase mapping.

🧩 Final Thought

You’re not just building an ETL engine—you’re modeling semantic gravity in your data graph. Nodes like ArtistCredit are gravitational centers, pulling in traversal weight from all directions. Others orbit more loosely, touched only by specific flows.

If you’d like, I can help you:

• Build a scoring model that blends schema and traversal

• Simulate ETL phases based on graph layering

• Visualize your graph with centrality overlays