Learning Graph Quality Metrics Report
Overview
- Total Concepts: 300
- Foundational Concepts (no dependencies): 1
- Concepts with Dependencies: 299
- Average Dependencies per Concept: 1.62
Graph Structure Validation
- Valid DAG Structure: ❌ No
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts
These concepts have no prerequisites:
- 1: Control System
Dependency Chain Analysis
- Maximum Dependency Chain Length: 18
Longest Learning Path:
- Control System (ID: 1)
- Dynamic System (ID: 13)
- Linear System (ID: 14)
- LTI System (ID: 16)
- Transfer Function (ID: 56)
- Block Diagram (ID: 122)
- Cascade Connection (ID: 125)
- Block Diagram Reduction (ID: 128)
- Closed-Loop Transfer (ID: 136)
- Forward Path (ID: 130)
- Loop (ID: 132)
- Loop Gain (ID: 135)
- Root Locus (ID: 170)
- Root Locus Rules (ID: 171)
- Magnitude Condition (ID: 178)
- Root Locus Gain (ID: 187)
- Gain Adjustment (ID: 188)
- Conditionally Stable (ID: 244)
Orphaned Nodes Analysis
- Total Orphaned Nodes: 125
Concepts that are not prerequisites for any other concept:
- 7: Actuator
- 17: Superposition Principle
- 18: Homogeneity
- 19: Causality
- 23: Higher-Order System
- 29: Zero-Input Response
- 30: Zero-State Response
- 37: Undamped System
- 39: Critically Damped System
- 40: Overdamped System
- 42: Percent Overshoot
- 45: Peak Time
- 46: Delay Time
- 50: Parabolic Input
- 52: Unit Step Response
- 54: Ramp Response
- 55: Standard Test Inputs
- 60: Time Domain
- 65: Pole-Zero Cancellation
- 69: Real Poles
...and 105 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 | 56 | Transfer Function | 15 |
| 2 | 150 | Stability | 14 |
| 3 | 171 | Root Locus Rules | 13 |
| 4 | 198 | Bode Plot | 13 |
| 5 | 1 | Control System | 10 |
| 6 | 62 | Poles | 10 |
| 7 | 122 | Block Diagram | 9 |
| 8 | 6 | Controller | 8 |
| 9 | 20 | Differential Equation | 8 |
| 10 | 59 | S-Domain | 8 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 1 |
| 1 | 134 |
| 2 | 147 |
| 3 | 15 |
| 4 | 3 |
Recommendations
- ⚠️ Many orphaned nodes (125): Consider if these should be prerequisites for advanced concepts
- ℹ️ Long dependency chains (18): Ensure students can follow extended learning paths
Report generated by learning-graph-reports/analyze_graph.py