Learning Graph Quality Metrics
Analysis Date: 2025-11-13
Total Concepts: 200
Summary Statistics
- Foundational Concepts (zero dependencies): 1
- Concepts with Dependencies: 199
- Average Dependencies per Concept: 1.31
- Maximum Dependency Chain Length: 11
- Orphaned Nodes (nothing depends on them): 112
Foundational Concepts
These concepts have no prerequisites and serve as entry points:
- 1: Real Numbers
Top 10 Most Depended-Upon Concepts
These concepts are prerequisites for many other concepts:
| Rank | ConceptID | Label | Indegree |
|---|---|---|---|
| 1 | 26 | Signals | 28 |
| 2 | 131 | Filters | 19 |
| 3 | 27 | Systems | 19 |
| 4 | 1 | Real Numbers | 13 |
| 5 | 98 | Fourier Transform | 8 |
| 6 | 29 | Discrete-Time Signals | 7 |
| 7 | 117 | Z-Transform | 6 |
| 8 | 100 | Discrete Fourier Transform | 6 |
| 9 | 90 | Quantization | 6 |
| 10 | 82 | Sampling Rate | 6 |
Orphaned Nodes (Potential Dead Ends)
These concepts have dependencies but nothing depends on them:
- 5: Phasors
- 11: Differential Equations
- 12: Partial Derivatives
- 18: Standard Deviation
- 21: Logarithmic Functions
- 22: Series and Sequences
- 23: Eigenvalues and Eigenvectors
- 24: Inner Product
- 25: Norms and Metrics
- 30: Analog Signals
- 33: Aperiodic Signals
- 34: Even Signals
- 35: Odd Signals
- 36: Energy Signals
- 37: Power Signals
- 40: Sinusoidal Signals
- 41: Exponential Signals
- 43: Time Shifting
- 44: Time Scaling
- 45: Signal Amplitude
Quality Assessment
Overall Quality Score: 75/100 - ACCEPTABLE
Issues Identified
- Many orphaned nodes (112), these should lead to higher-level concepts
- Low average dependencies (1.31), graph may be too linear
Recommendations
- The graph is a valid DAG (no cycles detected)
- Dependencies represent meaningful prerequisite relationships
- Multiple learning pathways exist through the material
- Start learning with any of the 1 foundational concepts