Learning Graph Quality Metrics Report

Overview

• Total Concepts: 326
• Foundational Concepts (no prerequisites, other concepts depend on them): 3
• Terminal Nodes (nothing depends on them, but have prerequisites): 96
• Orphaned Nodes (completely disconnected, no edges): 0
• Concepts with Dependencies: 323
• Average Dependencies per Concept: 1.64

Graph Structure Validation

• Valid DAG Structure: ✅ Yes
• Self-Dependencies: None detected ✅
• Cycles Detected: 0

Foundational Concepts

These concepts have no prerequisites:

• 1: Personal Agent
• 23: MicroPython Review
• 107: Sound Wave

Dependency Chain Analysis

• Maximum Dependency Chain Length: 21

Longest Learning Path:

1. Sound Wave (ID: 107)
2. Sampling (ID: 110)
3. Bit Depth (ID: 112)
4. Analog to Digital Conversion (ID: 115)
5. I2S Bus (ID: 116)
6. machine.I2S Class (ID: 120)
7. I2S Receive (ID: 121)
8. Audio Buffer (ID: 123)
9. Audio Frame (ID: 125)
10. RMS Loudness (ID: 156)
11. Noise Floor (ID: 183)
12. Speech Floor Gate (ID: 186)
13. Level Gate (ID: 187)
14. Utterance Boundaries (ID: 193)
15. Voice Activity Detection (ID: 194)
16. Wake Word (ID: 197)
17. Template Matching (ID: 201)
18. Template Correlation (ID: 202)
19. Detection Threshold (ID: 209)
20. False Accept (ID: 210)
21. Threshold Trade-Off (ID: 212)

Terminal Nodes Analysis

Terminal nodes are concepts that nothing else depends on but have prerequisites. They represent natural endpoints of learning paths — culminating or specialized concepts.

• Total Terminal Nodes: 96 (29.4% of all concepts)
• Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

• 2: Chatbot Versus Agent
• 12: Agent Progression Levels
• 19: Agent Data Flow
• 21: Agent Memory
• 24: Thonny IDE
• 36: Heap Fragmentation
• 42: Boot and Main Scripts
• 47: SRAM
• 58: Dupont Wires
• 62: Kit Bill of Materials
• 64: Power Supply Noise
• 77: Text Rendering
• 81: Hand Drawing
• 83: Sprite
• 87: Round Display Mask
• 89: Backlight Control
• 90: Display Refresh Rate
• 96: Long Press
• 102: Button Interrupt
• 105: Settings Screen

...and 76 more

Orphaned Nodes Analysis

Orphaned nodes are completely disconnected concepts with no inbound AND no outbound edges. These indicate a quality problem — every concept should connect to the graph.

• Total Orphaned Nodes: 0

✅ No orphaned nodes detected. All concepts are connected to the graph.

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	23	MicroPython Review	11
2	141	FFT	9
3	1	Personal Agent	8
4	9	Buddy Server	8
5	33	Timer	8
6	30	GPIO Pin	7
7	43	Raspberry Pi Pico 2 W	7
8	56	Push Button	7
9	73	Direct Region Write	7
10	224	HTTP Protocol	7

Outdegree Distribution

Dependencies	Number of Concepts
0	3
1	145
2	157
3	15
4	3
5	3

Recommendations

• ✅ Terminal node percentage (29.4%): Within healthy range (5-40%)
• ✅ DAG structure verified: Graph supports valid learning progressions
• ℹ️ Long dependency chains (21): Ensure students can follow extended learning paths

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Report generated by learning-graph-reports/analyze_graph.py