Learning Graph Quality Metrics Report
Overview
- Total Concepts: 200
- Foundational Concepts (no dependencies): 8
- Concepts with Dependencies: 192
- Average Dependencies per Concept: 1.78
Graph Structure Validation
- Valid DAG Structure: ❌ No
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts
These concepts have no prerequisites:
- 1: Point
- 14: Inductive Reasoning
- 47: Compass Construction
- 48: Straightedge Construction
- 55: Translation
- 56: Rotation
- 57: Reflection
- 58: Dilation
Dependency Chain Analysis
- Maximum Dependency Chain Length: 10
Longest Learning Path:
- Point (ID: 1)
- Line (ID: 2)
- Polygon (ID: 105)
- Quadrilateral (ID: 109)
- Parallelogram (ID: 110)
- Rectangle (ID: 111)
- Area of Rectangle (ID: 161)
- Volume of Prism (ID: 187)
- Optimization Problem (ID: 197)
- Design Challenge (ID: 199)
Orphaned Nodes Analysis
- Total Orphaned Nodes: 106
Concepts that are not prerequisites for any other concept:
- 7: Vertex
- 8: Collinear Points
- 9: Coplanar Points
- 13: Skew Lines
- 19: Hypothesis
- 20: Conclusion
- 22: Inverse
- 23: Contrapositive
- 24: Biconditional Statement
- 31: Indirect Proof
- 36: Complementary Angles
- 37: Supplementary Angles
- 39: Vertical Angles
- 40: Linear Pair
- 46: Midpoint Formula
- 49: Copying a Segment
- 50: Copying an Angle
- 51: Bisecting a Segment
- 52: Bisecting an Angle
- 53: Constructing Perpendiculars
...and 86 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 | 6 | Angle | 29 |
| 2 | 141 | Circle | 23 |
| 3 | 5 | Line Segment | 19 |
| 4 | 84 | Triangle | 17 |
| 5 | 2 | Line | 14 |
| 6 | 105 | Polygon | 14 |
| 7 | 1 | Point | 13 |
| 8 | 121 | Similar Figures | 11 |
| 9 | 173 | Prism | 8 |
| 10 | 26 | Theorem | 7 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 8 |
| 1 | 62 |
| 2 | 112 |
| 3 | 17 |
| 4 | 1 |
Recommendations
- ⚠️ Many orphaned nodes (106): Consider if these should be prerequisites for advanced concepts
Report generated by learning-graph-reports/analyze_graph.py