Learning Graph Quality Metrics Report¶
Overview¶
- Total Concepts: 221
- Foundational Concepts (no prerequisites, other concepts depend on them): 4
- Terminal Nodes (nothing depends on them, but have prerequisites): 97
- Orphaned Nodes (completely disconnected, no edges): 0
- Concepts with Dependencies: 217
- Average Dependencies per Concept: 1.57
Graph Structure Validation¶
- Valid DAG Structure: ✅ Yes
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts¶
These concepts have no prerequisites:
- 1: Learning Sciences
- 3: Cognitive Science
- 10: Generative AI
- 15: Markdown Authoring
Dependency Chain Analysis¶
- Maximum Dependency Chain Length: 10
Longest Learning Path:¶
- Learning Sciences (ID: 1)
- Seven Domains (ID: 16)
- Understanding Domain (ID: 18)
- Long-Term Memory (ID: 50)
- Semantic Memory (ID: 51)
- Schema (ID: 54)
- Mental Model (ID: 88)
- Novel Problem Solving (ID: 84)
- Problem-Based Learning (ID: 90)
- Scenario-Based Assessment (ID: 94)
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: 97 (43.9% of all concepts)
- Healthy Range: 5-40% of total concepts
Concepts at the end of learning paths:
- 5: Neuroscience in Learning
- 27: Autonomy Need
- 28: Competence Need
- 30: Flow State
- 31: Goal Orientation
- 33: Fixed Mindset
- 37: Attention Capture
- 38: Sustained Attention
- 40: Interest Development
- 41: ARCS Model
- 43: Iconic Memory
- 44: Echoic Memory
- 47: Phonological Loop
- 48: Visuospatial Sketchpad
- 49: Central Executive
- 52: Episodic Memory
- 55: Schema Construction
- 59: Elaboration
- 61: Multimedia Learning Theory
- 68: Testing Effect
...and 77 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 | 155 | Skill Invocation | 14 |
| 2 | 170 | MicroSim | 14 |
| 3 | 135 | Intelligent Textbook Design | 11 |
| 4 | 50 | Long-Term Memory | 10 |
| 5 | 16 | Seven Domains | 8 |
| 6 | 45 | Working Memory | 8 |
| 7 | 67 | Retrieval Practice | 8 |
| 8 | 15 | Markdown Authoring | 7 |
| 9 | 95 | Expertise | 7 |
| 10 | 121 | Learning Environment | 7 |
Outdegree Distribution¶
| Dependencies | Number of Concepts |
|---|---|
| 0 | 4 |
| 1 | 103 |
| 2 | 106 |
| 3 | 7 |
| 4 | 1 |
Recommendations¶
- ℹ️ High terminal node percentage (43.9%): Consider if some terminal concepts should be prerequisites for advanced concepts
- ✅ DAG structure verified: Graph supports valid learning progressions
Report generated by learning-graph-reports/analyze_graph.py