Weighted Graph Analysis

 

🏗️ Weighted Graph Analysis of create_new.sql Schema (with Euler-style Normalization)

Absolutely! Here’s a step-by-step approach to your request, combining SQL schema analysis, graph construction, attribute-based weighting, and a normalization step inspired by Euler ratios.

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1. Extract Entities and Attributes from create_new.sql

Below is a simplified mapping of main entities and their attributes (excluding join tables and pure FKs):

Table	Attributes (excluding IDs/FKs)	Total Attributes
area	area_id, name, gid	3
artist	artist_id, name, gid	3
artist_credit	artist_credit_id, name	2
base_type	table_id, gid, name, childOrder, parent, type_id	6
genre	genre_id, gid, genreName	3
instrument	instrument_id, gid, name	3
label	label_id, gid, labelCode, name	4
medium	medium_id, name	2
medium_format	description, hasDiscId, gid, medium_format_id, name, parent, year	7
recording	recording_id, gid, name	3
release	release_id, gid, name	3
release_group	release_group_id, gid, name	3
track	track_id, gid, name	3
work	work_id, gid, name	3

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2. Generate Graphviz DOT with Attributes as Vertex Weights

Each vertex represents an entity, labeled with its attribute count (weight).
Edges represent primary foreign key relationships in the schema.

3. Transform Unweighted to Weighted Graph

• Vertex Weight: Number of attributes (as above).
• Edge Weight: Optionally, sum or mean of incident vertex weights.

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4. Normalize Vertex Weights (Euler Ratio Inspired)

Let’s normalize all vertex weights to [0, 1] range (Euler-style):

• Let:
  w_min = 2 (minimum attributes)
  w_max = 7 (maximum attributes)

• Formula:
  norm_w = (w - w_min) / (w_max - w_min)

Table	Raw w	Normalized (norm_w)
area	3	0.2
artist	3	0.2
artist_credit	2	0.0
base_type	6	0.8
genre	3	0.2
instrument	3	0.2
label	4	0.4
medium	2	0.0
medium_format	7	1.0
recording	3	0.2
release	3	0.2
release_group	3	0.2
track	3	0.2
work	3	0.2

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5. Graphviz with Normalized Weights

6. Penalty & CsvFileProcessingPriority Analogy

• Penalty: Use normalized weight as a “processing penalty”. (Higher = more attributes = more expensive to process.)
• CsvFileProcessingPriority:
  Replace the simple count of outgoing edges with normalized vertex weight in the priority formula:
  priority = outgoing_edges * (1 + normalized_weight)

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7. Summary

• Visualize attribute complexity and normalize for cross-entity comparison.
• Use these normalized values in processing priorities for ETL or CSV import.
• Euler-style normalization gives you a fair, proportionate ranking for processing and graph analysis.