Learning Graph Quality Metrics Report
Overview
- Total Concepts: 300
- Foundational Concepts (no dependencies): 2
- Concepts with Dependencies: 298
- Average Dependencies per Concept: 1.71
Graph Structure Validation
- Valid DAG Structure: ❌ No
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts
These concepts have no prerequisites:
- 1: Scalar
- 74: Function
Dependency Chain Analysis
- Maximum Dependency Chain Length: 19
Longest Learning Path:
- Scalar (ID: 1)
- Vector (ID: 2)
- Vector Notation (ID: 3)
- Vector Addition (ID: 7)
- Linear Combination (ID: 19)
- Span (ID: 20)
- Linear Independence (ID: 21)
- Basis Vector (ID: 23)
- Vector Space (ID: 26)
- Linear Transformation (ID: 75)
- Transformation Matrix (ID: 76)
- Eigenvalue (ID: 114)
- Eigenvector (ID: 115)
- Eigenspace (ID: 119)
- Diagonalization (ID: 122)
- PCA (ID: 175)
- Principal Component (ID: 176)
- Variance Explained (ID: 177)
- Scree Plot (ID: 178)
Orphaned Nodes Analysis
- Total Orphaned Nodes: 97
Concepts that are not prerequisites for any other concept:
- 9: Vector Subtraction
- 11: Cross Product
- 14: Vector Normalization
- 16: L1 Norm
- 17: L2 Norm
- 18: L-Infinity Norm
- 22: Linear Dependence
- 27: Dimension of Space
- 34: Matrix Addition
- 49: Dense Matrix
- 50: Block Matrix
- 58: Row Scaling
- 59: Row Addition
- 65: Basic Variable
- 67: Unique Solution
- 68: Infinite Solutions
- 69: No Solution
- 71: Trivial Solution
- 73: Back Substitution
- 81: 2D Rotation
...and 77 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 | 28 | Matrix | 25 |
| 2 | 2 | Vector | 18 |
| 3 | 37 | Matrix Multiplication | 13 |
| 4 | 10 | Dot Product | 9 |
| 5 | 186 | Gradient Descent | 9 |
| 6 | 76 | Transformation Matrix | 8 |
| 7 | 101 | Determinant | 8 |
| 8 | 5 | 3D Vector | 7 |
| 9 | 12 | Vector Magnitude | 7 |
| 10 | 75 | Linear Transformation | 7 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 2 |
| 1 | 103 |
| 2 | 180 |
| 3 | 14 |
| 4 | 1 |
Recommendations
- ⚠️ Many orphaned nodes (97): Consider if these should be prerequisites for advanced concepts
- ℹ️ Long dependency chains (19): Ensure students can follow extended learning paths
Report generated by learning-graph-reports/analyze_graph.py