Learning Graph Quality Metrics Report
Overview
- Total Concepts: 300
- Foundational Concepts (no dependencies): 4
- Concepts with Dependencies: 296
- Average Dependencies per Concept: 2.12
Graph Structure Validation
- Valid DAG Structure: Yes
- Self-Dependencies: None detected
- Cycles Detected: 0
Foundational Concepts
These concepts have no prerequisites:
- 1: Electric Charge
- 10: Circuit Schematic Symbols
- 110: Period
- 118: Complex Numbers
Dependency Chain Analysis
- Maximum Dependency Chain Length: 21
Longest Learning Path:
- Electric Charge (ID: 1)
- Current (ID: 3)
- Magnetic Field (ID: 69)
- Inductor (ID: 67)
- Inductance (ID: 68)
- Inductive Reactance (ID: 128)
- Reactance (ID: 126)
- Complex Impedance (ID: 133)
- Impedance (ID: 125)
- AC Circuit Analysis (ID: 134)
- Transfer Function (ID: 157)
- Frequency Response (ID: 156)
- Cutoff Frequency (ID: 166)
- Bandwidth (ID: 169)
- Quality Factor (ID: 177)
- Resonance (ID: 175)
- Band-Pass Filter (ID: 184)
- Second-Order Filter (ID: 188)
- Filter Order (ID: 189)
- Filter Design (ID: 197)
- Audio Tone Control (ID: 198)
Orphaned Nodes Analysis
- Total Orphaned Nodes: 110
Concepts that are not prerequisites for any other concept (terminal/application concepts):
- 13: Dependent Sources
- 16: Series-Parallel Circuits
- 17: Voltage Divider
- 18: Current Divider
- 25: Open Circuit
- 26: Short Circuit
- 28: Energy Conservation
- 29: SI Units for Circuits
- 38: Source Transformation
- 42: Norton Equivalent
- 49: Circuit Simplification
- 50: Nodal Analysis
- 51: Mesh Analysis
- 52: Two-Port Networks
- 58: Resistor Tolerance
- 59: Potentiometer
- 62: Parallel Plate Capacitor
- 65: Capacitors in Series
- 71: Inductors in Series
- 72: Inductors in Parallel
- 74: Coupling Coefficient
- 75: Wire Resistance
- 76: Parasitic Capacitance
- 77: Parasitic Inductance
- 79: Component Derating
- 81: Transient Response
- 92: Final Conditions
- 99: Overdamped Response
- 100: Underdamped Response
- 101: Critically Damped Response
...and 80 more
Indegree Analysis
Top 10 concepts that are prerequisites for the most other concepts:
| Rank | ID | Concept Label | Indegree |
|---|---|---|---|
| 1 | 3 | Current | 21 |
| 2 | 2 | Voltage | 19 |
| 3 | 6 | Resistance | 18 |
| 4 | 201 | Operational Amplifier | 16 |
| 5 | 56 | Resistor | 13 |
| 6 | 109 | Frequency | 12 |
| 7 | 277 | Oscilloscope | 12 |
| 8 | 5 | Power | 11 |
| 9 | 84 | RC Circuit | 11 |
| 10 | 231 | Signal | 11 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 4 |
| 1 | 50 |
| 2 | 175 |
| 3 | 59 |
| 4 | 10 |
| 5 | 2 |
Quality Score
Overall Quality Score: 100/100
Recommendations
- DAG structure verified: Graph supports valid learning progressions
- Long dependency chains (21): Ensures deep learning paths
- 110 terminal concepts: Many concepts serve as endpoints for applied learning
Report generated by learning-graph-generator skill