Learning Graph Quality Metrics Report
Overview
- Total Concepts: 200
- Foundational Concepts (no dependencies): 10
- Concepts with Dependencies: 190
- Average Dependencies per Concept: 1.83
Graph Structure Validation
- Valid DAG Structure: ❌ No
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts
These concepts have no prerequisites:
- 1: Complex Numbers
- 4: Sine Wave
- 33: Jean Baptiste Fourier
- 73: Microcontroller
- 94: Fixed Point Arithmetic
- 105: C Language
- 111: Assembly Language
- 114: Python Language
- 133: Benchmarking
- 177: Data Visualization
Dependency Chain Analysis
- Maximum Dependency Chain Length: 15
Longest Learning Path:
- Sine Wave (ID: 4)
- Cosine Wave (ID: 5)
- Periodic Functions (ID: 9)
- Harmonics (ID: 10)
- Fourier Series (ID: 34)
- Continuous Fourier Transform (ID: 35)
- Discrete Fourier Transform (ID: 36)
- DFT Definition (ID: 37)
- DFT Complexity (ID: 38)
- FFT Algorithm (ID: 49)
- FFT History (ID: 50)
- Cooley Tukey Algorithm (ID: 51)
- Radix-2 FFT (ID: 52)
- Radix-4 FFT (ID: 53)
- Split Radix FFT (ID: 54)
Orphaned Nodes Analysis
- Total Orphaned Nodes: 76
Concepts that are not prerequisites for any other concept:
- 11: Complex Conjugate
- 13: Unit Circle
- 14: Hertz
- 22: Aliasing
- 24: Bit Depth
- 25: ADC Conversion
- 27: Signal To Noise Ratio
- 30: Band Pass Filter
- 32: Spectral Leakage
- 43: Power Spectrum
- 48: Orthogonality
- 54: Split Radix FFT
- 57: Twiddle Factors
- 59: In Place FFT
- 60: Decimation In Time
- 61: Decimation In Frequency
- 62: FFT Stages
- 64: O(N log N)
- 66: Power Of Two Sizes
- 67: Real FFT
...and 56 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 | 49 | FFT Algorithm | 21 |
| 2 | 7 | Frequency | 10 |
| 3 | 16 | Frequency Domain | 9 |
| 4 | 121 | FFT Libraries | 9 |
| 5 | 4 | Sine Wave | 8 |
| 6 | 17 | Analog Signals | 8 |
| 7 | 52 | Radix-2 FFT | 8 |
| 8 | 73 | Microcontroller | 8 |
| 9 | 134 | Performance Metrics | 8 |
| 10 | 1 | Complex Numbers | 7 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 10 |
| 1 | 53 |
| 2 | 118 |
| 3 | 17 |
| 4 | 2 |
Recommendations
- ⚠️ Many orphaned nodes (76): Consider if these should be prerequisites for advanced concepts
Report generated by learning-graph-reports/analyze_graph.py