Learning Graph Quality Metrics Report
Overview
- Total Concepts: 200
- Foundational Concepts (no dependencies): 7
- Concepts with Dependencies: 193
- Average Dependencies per Concept: 1.48
Graph Structure Validation
- Valid DAG Structure:Yes ✅
- Self-Dependencies: None detected ✅
- Cycles Detected: 0 ✅
Foundational Concepts
These concepts have no prerequisites:
- 1: Scientific Method
- 18: Trigonometry for Physics
- 19: Proportional Reasoning
- 40: Inertia
- 66: Potential Energy
- 115: Mechanical Waves
- 181: Electric Charge
Dependency Chain Analysis
- Maximum Dependency Chain Length: 17
Longest Learning Path:
- Scientific Method (ID: 1)
- Measurement (ID: 2)
- Scalars (ID: 9)
- Vectors (ID: 10)
- Displacement (ID: 20)
- Velocity (ID: 23)
- Acceleration (ID: 24)
- Simple Harmonic Motion (ID: 101)
- Period (ID: 104)
- Frequency (ID: 105)
- Wave Frequency (ID: 120)
- Wave Speed (ID: 122)
- Speed of Light (ID: 148)
- Index of Refraction (ID: 160)
- Snell's Law (ID: 159)
- Total Internal Reflection (ID: 161)
- Critical Angle (ID: 162)
Orphaned Nodes Analysis
- Total Orphaned Nodes: 90
Concepts that are not prerequisites for any other concept:
- 8: Precision vs Accuracy
- 12: Vector Subtraction
- 14: Dot Product
- 15: Cross Product
- 28: Position-Time Graphs
- 29: Velocity-Time Graphs
- 30: Acceleration-Time Graphs
- 31: Kinematic Equations
- 32: Free Fall
- 34: Horizontal Projection
- 35: Angled Projection
- 39: Newton's First Law
- 46: Dynamic Equilibrium
- 48: Static Friction
- 49: Kinetic Friction
- 50: Coefficient of Friction
- 56: Atwood Machine
- 57: Pulley Systems
- 60: Banked Curves
- 62: Work by Constant Force
...and 70 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 | 37 | Force | 17 |
| 2 | 181 | Electric Charge | 11 |
| 3 | 10 | Vectors | 8 |
| 4 | 115 | Mechanical Waves | 8 |
| 5 | 134 | Sound Waves | 8 |
| 6 | 2 | Measurement | 7 |
| 7 | 23 | Velocity | 7 |
| 8 | 145 | Light Waves | 7 |
| 9 | 163 | Lenses | 7 |
| 10 | 24 | Acceleration | 6 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 7 |
| 1 | 102 |
| 2 | 90 |
| 3 | 1 |
Recommendations
- ⚠️ Many orphaned nodes (90): Consider if these should be prerequisites for advanced concepts
- ℹ️ Long dependency chains (17): 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