Learning Graph Quality Metrics Report¶
Overview¶
- Total Concepts: 368
- Foundational Concepts (no prerequisites, other concepts depend on them): 1
- Terminal Nodes (nothing depends on them, but have prerequisites): 163
- Orphaned Nodes (completely disconnected, no edges): 0
- Concepts with Dependencies: 367
- Average Dependencies per Concept: 1.45
Graph Structure Validation¶
- Valid DAG Structure: ✅ Yes
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts¶
These concepts have no prerequisites:
- 1: South Asia
Dependency Chain Analysis¶
- Maximum Dependency Chain Length: 30
Longest Learning Path:¶
- South Asia (ID: 1)
- Indian Subcontinent (ID: 2)
- Himalaya (ID: 4)
- Indus River (ID: 6)
- Mehrgarh (ID: 18)
- Indus Valley Civilization (ID: 19)
- Indo-Aryan Migration (ID: 22)
- Vedic Period (ID: 23)
- Mahajanapadas (ID: 26)
- Maurya Empire (ID: 28)
- Sangam Age (ID: 32)
- Indian Ocean Trade (ID: 35)
- European Traders (ID: 50)
- East India Company (ID: 51)
- Battle of Plassey (ID: 52)
- Revolt of 1857 (ID: 53)
- British Raj (ID: 54)
- Indian National Congress (ID: 58)
- Partition of 1947 (ID: 64)
- Radcliffe Line (ID: 65)
- Partition Migration (ID: 66)
- Diaspora (ID: 334)
- Punjabi Pioneers in California (ID: 342)
- Bhagat Singh Thind Case (ID: 343)
- Immigration Act of 1965 (ID: 344)
- Model Minority Myth (ID: 346)
- Stereotypes (ID: 353)
- Allyship (ID: 362)
- Community Organizing (ID: 364)
- Community Impact (ID: 365)
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: 163 (44.3% of all concepts)
- Healthy Range: 5-40% of total concepts
Concepts at the end of learning paths:
- 11: Western and Eastern Ghats
- 12: Thar Desert
- 14: Bay of Bengal
- 20: Harappa and Mohenjo-daro
- 21: Indus Script
- 34: Nalanda
- 36: Chola Dynasty
- 40: Vijayanagara Empire
- 48: Maratha Empire
- 57: Bengal Famine of 1943
- 67: Kashmir Dispute
- 83: Langar
- 85: Zoroastrians (Parsis)
- 86: Jewish Communities
- 101: Devanagari
- 102: Gurmukhi
- 109: Holi
- 111: Dashain and Tihar
- 114: Eid al-Adha
- 115: Ashura
...and 143 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 | 54 | British Raj | 15 |
| 2 | 35 | Indian Ocean Trade | 12 |
| 3 | 46 | Indo-Persian Culture | 11 |
| 4 | 71 | Hinduism | 11 |
| 5 | 4 | Himalaya | 9 |
| 6 | 106 | Lunisolar Calendar | 9 |
| 7 | 160 | Classical Dance | 8 |
| 8 | 190 | Cotton in South Asia | 8 |
| 9 | 17 | Regional Diversity | 7 |
| 10 | 25 | Sanskrit | 7 |
Outdegree Distribution¶
| Dependencies | Number of Concepts |
|---|---|
| 0 | 1 |
| 1 | 209 |
| 2 | 153 |
| 3 | 4 |
| 4 | 1 |
Recommendations¶
- ℹ️ High terminal node percentage (44.3%): Consider if some terminal concepts should be prerequisites for advanced concepts
- ✅ DAG structure verified: Graph supports valid learning progressions
- ℹ️ Long dependency chains (30): Ensure students can follow extended learning paths
- ℹ️ Consider adding cross-dependencies: More connections could create richer learning pathways
Report generated by learning-graph-reports/analyze_graph.py