Learning Graph Quality Metrics Report
Overview
- Total Concepts: 574
- Foundational Concepts (no dependencies): 14
- Concepts with Dependencies: 560
- Average Dependencies per Concept: 1.56
Graph Structure Validation
- Valid DAG Structure: ✅ Yes
- 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
- 201: Thonny IDE
- 257: MEMS Microphone
- 290: Productive Failure
- 344: Ground Truth
Dependency Chain Analysis
- Maximum Dependency Chain Length: 30
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 Complexity (ID: 63)
- FFT Size (ID: 65)
- Frame Duration (ID: 359)
- Processing Deadline (ID: 360)
- Motivation For Optimization (ID: 362)
- Divide And Conquer (ID: 363)
- Even Odd Split (ID: 364)
- Recursive Decomposition (ID: 365)
- Subproblem (ID: 366)
- Recombination Step (ID: 367)
- Butterfly Structure (ID: 384)
- Butterfly Pair (ID: 387)
- Stage Span (ID: 388)
- Stage Loop (ID: 391)
- Work Split Strategy (ID: 525)
- Hot Loop (ID: 528)
- Special Case Optimization (ID: 529)
- Optimization Attribution (ID: 540)
- Optimization Composition (ID: 559)
- Sub Linear Composition (ID: 560)
Orphaned Nodes Analysis
- Total Orphaned Nodes: 185
Concepts that are not prerequisites for any other concept:
- 14: Hertz
- 25: ADC Conversion
- 27: Signal To Noise Ratio
- 30: Band Pass Filter
- 54: Split Radix FFT
- 60: Decimation In Time
- 61: Decimation In Frequency
- 67: Real FFT
- 70: IFFT Algorithm
- 72: FFT Scaling
- 81: RP2350 Chip
- 83: General Purpose CPU
- 88: Embedded Systems
- 93: Saturating Arithmetic
- 100: Q31 Format
- 101: Hardware Multiplier
- 107: GCC Compiler
- 108: ARM Compiler
- 116: SciPy FFT
- 120: Disassembly
...and 165 more
Connected Components
- Number of Connected Components: 2
⚠️ Multiple disconnected subgraphs detected:
Component 1 (573 concepts)
- Complex Numbers
- Imaginary Unit
- Euler's Formula
- Sine Wave
- Cosine Wave
- Amplitude
- Frequency
- Phase
- Periodic Functions
- Harmonics
- ...and 563 more
Component 2 (1 concepts)
- Productive Failure
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 | 13 |
| 3 | 4 | Sine Wave | 10 |
| 4 | 16 | Frequency Domain | 9 |
| 5 | 73 | Microcontroller | 9 |
| 6 | 121 | FFT Libraries | 9 |
| 7 | 1 | Complex Numbers | 8 |
| 8 | 17 | Analog Signals | 8 |
| 9 | 52 | Radix-2 FFT | 8 |
| 10 | 74 | ARM Architecture | 8 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 14 |
| 1 | 267 |
| 2 | 274 |
| 3 | 17 |
| 4 | 2 |
Recommendations
- ⚠️ Connect disconnected components: Add dependencies to link separate subgraphs
- ⚠️ Many orphaned nodes (185): Consider if these should be prerequisites for advanced concepts
- ✅ DAG structure verified: Graph supports valid learning progressions
- ℹ️ Long dependency chains (30): Ensure students can follow extended learning paths
Report generated by learning-graph-reports/analyze_graph.py