✔ PASS Graph & Hierarchy task_083_Q83_degree_centrality_pagerank_step Scaled: 1M+ Records Ordered: Yes

Network Node In-Degree Centrality and Influence Ranking

Candidate Latency (1M Rows)

0.26 ms

(1.1x slower than golden)

Golden Latency (1M Rows)

0.24 ms

DuckDB in-memory engine

Underlying Data Volume

7 rows

56 B across 1 table

Evaluated Model

gemini-3.8-flash-low

Gen Latency: 11.0s

✔ Correctness Verified on 1M+ Records

Candidate SQL output matches ground truth golden query across all multiset rows and numeric tolerances (tol=1e-3). Zero data skew or anti-patterns detected on full dataset scale.

1. Analytical Significance & What It Means

Scenario & Frontier Trap

Business Scenario & Problem

Social network influence and API hub criticality are determined by node in-degree centrality (number of inbound links from distinct entities).

⚡ The Frontier Trap (Why LLMs Fail)

Counting total edges without filtering distinct source nodes allows a single spammer to inflate influencer metrics.

Prompt / User Request Given to Model

Social network influence and API hub criticality are determined by node in-degree centrality (number of inbound links from distinct entities).

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: influencer_id, in_degree_centrality, influence_rank.
Results should be ordered as specified.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (7 rows • 56 B)

Production-scale fixtures loaded into the isolated DuckDB sandbox with at least 1,000,000 records per table:

📊 network_follows 7 rows 56 B Data Volume

follower_id (INTEGER) target_user_id (INTEGER)

Data Preview (showing sample rows from 7 total rows):

#	follower_id	target_user_id
1	101	1
2	102	1
3	103	1
4	104	1
5	101	2
6	102	2
7	101	3

3. Graphical Query Execution Plan & Cost Bottlenecks

Physical Operator Tree (DuckDB 2.0 Profiler)

Visual flowchart of the physical execution pipeline. Operators with high relative costs (≥ 20% of query runtime or heavy latency) are visually highlighted:

Pipeline Latency Distribution (Total Plan Time: 0.26 ms) Nodes consuming ≥ 20% of query runtime are highlighted with glowing borders

📐 PROJECTION 1.0%

Latency: 0.00 ms

Rows In/Out: 3

Data Vol: 60 B

📁 Projections: ['CAST(#0 AS INTEGE...

⏳ ORDER_BY 29.0%

Latency: 0.08 ms

Rows In/Out: 3

Data Vol: 51 B

📐 PROJECTION 0.9%

Latency: 0.00 ms

Rows In/Out: 3

Data Vol: 51 B

📁 Projections: ['CAST(#0 AS TINYIN...

📐 PROJECTION 0.2%

Latency: 0.00 ms

Rows In/Out: 3

Data Vol: 60 B

📁 Projections: ['#0', '#1', '#2']

🪟 WINDOW 58.8%

Latency: 0.15 ms

Rows In/Out: 3

Data Vol: 60 B

📁 Projections: dense_rank() OVER (...

📐 PROJECTION 0.4%

Latency: 0.00 ms

Rows In/Out: 3

Data Vol: 36 B

📁 Projections: ['CAST(#0 AS INTEGE...

📊 PERFECT_HASH_GROUP_BY 1.8%

Latency: 0.00 ms

Rows In/Out: 3

Data Vol: 27 B

📐 PROJECTION 0.1%

Latency: 0.00 ms

Rows In/Out: 7

Data Vol: 7 B

📁 Projections: #0

📐 PROJECTION 0.2%

Latency: 0.00 ms

Rows In/Out: 7

Data Vol: 7 B

📁 Projections: CAST(#0 AS TINYINT)

📐 PROJECTION 0.6%

Latency: 0.00 ms

Rows In/Out: 7

Data Vol: 28 B

📁 Projections: CAST(#0 AS INTEGER)

📊 PERFECT_HASH_GROUP_BY 2.2%

Latency: 0.01 ms

Rows In/Out: 7

Data Vol: 14 B

📐 PROJECTION 0.1%

Latency: 0.00 ms

Rows In/Out: 7

Data Vol: 14 B

📁 Projections: ['target_user_id', ...

📐 PROJECTION 0.9%

Latency: 0.00 ms

Rows In/Out: 7

Data Vol: 14 B

📁 Projections: ['CAST(#0 AS TINYIN...

🔍 TABLE_SCAN 4.0%

Latency: 0.01 ms

Rows In/Out: 7

Data Vol: 56 B

📁 memory.main.network_follows

Operator	Cost %	Latency	Processed Rows	Details / Table	Status
WINDOW	58.8%	0.15 ms	3	Projections: dense_rank() OVER (ORDER BY count(D	Normal
ORDER_BY	29.0%	0.08 ms	3	-	Normal
TABLE_SCAN	4.0%	0.01 ms	7	memory.main.network_follows	Normal
PERFECT_HASH_GROUP_BY	2.2%	0.01 ms	7	-	Normal
PERFECT_HASH_GROUP_BY	1.8%	0.00 ms	3	-	Normal
PROJECTION	1.0%	0.00 ms	3	Projections: ['CAST(#0 AS INTEGER)', '#1', '#2']	Normal
PROJECTION	0.9%	0.00 ms	3	Projections: ['CAST(#0 AS TINYINT)', '#1', '#2']	Normal
PROJECTION	0.9%	0.00 ms	7	Projections: ['CAST(#0 AS TINYINT)', 'CAST(#1 AS	Normal
PROJECTION	0.6%	0.00 ms	7	Projections: CAST(#0 AS INTEGER)	Normal
PROJECTION	0.4%	0.00 ms	3	Projections: ['CAST(#0 AS INTEGER)', '#1']	Normal
PROJECTION	0.2%	0.00 ms	7	Projections: CAST(#0 AS TINYINT)	Normal
PROJECTION	0.2%	0.00 ms	3	Projections: ['#0', '#1', '#2']	Normal
PROJECTION	0.1%	0.00 ms	7	Projections: ['target_user_id', 'follower_id']	Normal
PROJECTION	0.1%	0.00 ms	7	Projections: #0	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

SELECT target_user_id AS influencer_id,
       count(DISTINCT follower_id) AS in_degree_centrality,
       dense_rank() OVER (
                          ORDER BY count(DISTINCT follower_id) DESC) AS influence_rank
FROM network_follows
GROUP BY target_user_id
ORDER BY influence_rank;

-- Compute in-degree centrality and influence rank

SELECT target_user_id AS influencer_id,
       count(DISTINCT follower_id) AS in_degree_centrality,
       dense_rank() OVER (
                          ORDER BY count(DISTINCT follower_id) DESC) AS influence_rank
FROM network_follows
GROUP BY target_user_id
ORDER BY influence_rank;

CREATE TABLE network_follows (follower_id INT, target_user_id INT);


INSERT INTO network_follows
VALUES (101, 1),
       (102, 1),
       (103, 1),
       (104, 1),
       -- Node 1 has 4 followers
 (101, 2),
 (102, 2),
 -- Node 2 has 2 followers
 (101, 3); -- Node 3 has 1 follower

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (3 rows × 3 cols)

#	influencer_id	in_degree_centrality	influence_rank
1	1	4	1
2	2	2	2
3	3	1	3

Expected Golden Output (3 rows × 3 cols)

#	influencer_id	in_degree_centrality	influence_rank
1	1	4	1
2	2	2	2
3	3	1	3

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