Learning Graph Quality Metrics Report

Overview

• Total Concepts: 253
• Foundational Concepts (no prerequisites, other concepts depend on them): 5
• Terminal Nodes (nothing depends on them, but have prerequisites): 38
• Orphaned Nodes (completely disconnected, no edges): 0
• Concepts with Dependencies: 248
• Average Dependencies per Concept: 2.58

Graph Structure Validation

• Valid DAG Structure: ✅ Yes
• Self-Dependencies: None detected ✅
• Cycles Detected: 0

Foundational Concepts

These concepts have no prerequisites:

• 1: Cell Membrane
• 2: Ion
• 3: Protein
• 4: Concentration Gradient
• 5: Nervous System

Dependency Chain Analysis

• Maximum Dependency Chain Length: 20

Longest Learning Path:

1. Cell Membrane (ID: 1)
2. Neuron (ID: 8)
3. Axon (ID: 11)
4. Myelin Sheath (ID: 13)
5. White Matter (ID: 66)
6. Spinal Cord (ID: 77)
7. Neural Tube (ID: 130)
8. Neurogenesis (ID: 131)
9. Neuronal Migration (ID: 132)
10. Synaptogenesis (ID: 133)
11. Synaptic Pruning (ID: 134)
12. Adolescent Brain (ID: 137)
13. Prefrontal Maturation (ID: 138)
14. Reward Sensitivity in Teens (ID: 139)
15. Decision-Making (ID: 192)
16. Reward Prediction Error (ID: 193)
17. Reward Pathway (ID: 229)
18. Addiction (ID: 230)
19. Opioids (ID: 233)
20. Naloxone (ID: 234)

Terminal Nodes Analysis

Terminal nodes are concepts that nothing else depends on but have prerequisites. They represent natural endpoints of learning paths: culminating or specialized concepts.

• Total Terminal Nodes: 38 (15.0% of all concepts)
• Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

• 18: Schwann Cell
• 38: Conduction Velocity
• 40: Local Anesthetic
• 41: Neurotoxin
• 44: Electrical Synapse
• 62: Myasthenia Gravis
• 90: Color Vision
• 98: Ventral and Dorsal Streams
• 99: Pituitary Tumor
• 109: Gustation
• 112: Gate Control Theory
• 113: Phantom Limb Pain
• 128: Levodopa
• 129: Deep Brain Stimulation
• 141: Fetal Alcohol Spectrum
• 170: Sleep Deprivation
• 171: Narcolepsy
• 183: Post-Traumatic Stress Disorder
• 202: Anti-Amyloid Antibody
• 206: Gene Therapy

...and 18 more

Orphaned Nodes Analysis

Orphaned nodes are completely disconnected concepts with no inbound AND no outbound edges. These indicate a quality problem: every concept should connect to the graph.

• Total Orphaned Nodes: 0

✅ No orphaned nodes detected. All concepts are connected to the graph.

Connected Components

• Number of Connected Components: 1

✅ All concepts are connected in a single graph.

Indegree Analysis

Top 10 concepts that are prerequisites for the most other concepts:

Rank	Concept ID	Concept Label	Indegree
1	6	Central Nervous System	18
2	8	Neuron	13
3	46	Neurotransmitter	13
4	67	Cerebral Cortex	13
5	3	Protein	11
6	34	Action Potential	10
7	57	Dopamine	10
8	74	Hypothalamus	9
9	77	Spinal Cord	9
10	1	Cell Membrane	8

Outdegree Distribution

Dependencies	Number of Concepts
0	5
1	19
2	98
3	104
4	24
5	2
6	1

Recommendations

• ✅ Terminal node percentage (15.0%): Within healthy range (5-40%)
• ✅ DAG structure verified: Graph supports valid learning progressions
• ℹ️ Long dependency chains (20): Ensure students can follow extended learning paths

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Report generated by learning-graph-reports/analyze_graph.py