Learning Graph Quality Metrics Report¶
Overview¶
- Total Concepts: 200
- Foundational Concepts (no dependencies): 1
- Concepts with Dependencies: 199
- Average Dependencies per Concept: 1.79
Graph Structure Validation¶
- Valid DAG Structure: ❌ No
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts¶
These concepts have no prerequisites:
- 1: Geography Definition
Dependency Chain Analysis¶
- Maximum Dependency Chain Length: 17
Longest Learning Path:¶
- Geography Definition (ID: 1)
- Map Reading Basics (ID: 2)
- Cardinal Directions (ID: 3)
- Latitude (ID: 11)
- Equator (ID: 13)
- Hemispheres (ID: 16)
- Continents (ID: 17)
- North America (ID: 18)
- United States Location (ID: 19)
- Population (ID: 152)
- Urban Areas (ID: 154)
- Metropolitan Areas (ID: 157)
- Major Cities (ID: 158)
- Manufacturing (ID: 176)
- Economic Geography (ID: 197)
- Environmental Issues (ID: 199)
- Conservation (ID: 200)
Orphaned Nodes Analysis¶
- Total Orphaned Nodes: 111
Concepts that are not prerequisites for any other concept:
- 4: Compass Rose
- 10: Topographic Maps
- 21: US Size Comparison
- 22: Time Zones
- 28: Hills
- 29: Deserts
- 31: Islands
- 32: Peninsulas
- 34: Appalachian Mountains
- 35: Sierra Nevada
- 38: Central Valley
- 39: Colorado Plateau
- 43: Missouri River
- 45: Columbia River
- 46: Ohio River
- 47: Rio Grande
- 48: Hudson River
- 51: Lake Superior
- 52: Lake Michigan
- 53: Lake Huron
...and 91 more
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 | 7 | Political Maps | 54 |
| 2 | 19 | United States Location | 18 |
| 3 | 87 | Southeast Region | 12 |
| 4 | 23 | Landforms | 11 |
| 5 | 88 | Midwest Region | 11 |
| 6 | 68 | Climate Zones | 10 |
| 7 | 1 | Geography Definition | 9 |
| 8 | 158 | Major Cities | 9 |
| 9 | 164 | Natural Resources | 9 |
| 10 | 2 | Map Reading Basics | 7 |
Outdegree Distribution¶
| Dependencies | Number of Concepts |
|---|---|
| 0 | 1 |
| 1 | 46 |
| 2 | 148 |
| 3 | 5 |
Recommendations¶
- ⚠️ Many orphaned nodes (111): Consider if these should be prerequisites for advanced concepts
- ℹ️ Long dependency chains (17): Ensure students can follow extended learning paths
Report generated by learning-graph-reports/analyze_graph.py