Learning Graph Quality Metrics Report

Overview

• Total Concepts: 531
• Foundational Concepts (no prerequisites, other concepts depend on them): 5
• Terminal Nodes (nothing depends on them, but have prerequisites): 204
• Orphaned Nodes (completely disconnected, no edges): 0
• Concepts with Dependencies: 526
• Average Dependencies per Concept: 1.37

Graph Structure Validation

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

Foundational Concepts

These concepts have no prerequisites:

• 1: Computational Thinking
• 7: Physical Computing
• 27: Raspberry Pi Foundation
• 49: Breadboard
• 57: Voltage

Dependency Chain Analysis

• Maximum Dependency Chain Length: 20

Longest Learning Path:

1. Raspberry Pi Foundation (ID: 27)
2. Raspberry Pi Pico (ID: 28)
3. GPIO Pin (ID: 53)
4. Analog Pin (ID: 56)
5. Analog To Digital Converter (ID: 80)
6. Analog Read (ID: 130)
7. Sound Sensor (ID: 141)
8. Microphone Array (ID: 443)
9. USB Microphone (ID: 444)
10. Audio Sampling Rate (ID: 445)
11. Analog Audio Signal (ID: 446)
12. Digital Audio Signal (ID: 447)
13. Fast Fourier Transform (ID: 449)
14. Frequency Spectrum (ID: 450)
15. Spectrogram (ID: 451)
16. Sound Classification (ID: 452)
17. Audio Model Inference (ID: 463)
18. Sound Event Detection (ID: 464)
19. Environmental Sound Class (ID: 465)
20. Alert Sound Trigger (ID: 466)

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: 204 (38.4% of all concepts)
• Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

• 15: Rubber Duck Debugging
• 37: RP2350 Chip
• 38: Broadcom BCM2712
• 51: Breadboard Row
• 64: Capacitor
• 66: LED Polarity
• 67: Forward Voltage
• 68: Current Limiting Resistor
• 71: 3.3 Volt Logic
• 72: Short Circuit
• 74: Series Circuit
• 75: Parallel Circuit
• 77: Continuity Test
• 82: Duty Cycle
• 85: Circuit Diagram
• 86: Wire Color Convention
• 87: Power Rail
• 88: Component Datasheet
• 89: Static Discharge
• 105: Chained LED Protocol

...and 184 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	57	Voltage	12
2	32	Raspberry Pi 5	11
3	53	GPIO Pin	10
4	58	Current	9
5	130	Analog Read	9
6	302	Bash Shell	9
7	65	LED	8
8	109	Frame Rate	8
9	222	DS3231 Module	7
10	258	IP Address	7

Outdegree Distribution

Dependencies	Number of Concepts
0	5
1	352
2	153
3	20
4	1

Recommendations

• ✅ Terminal node percentage (38.4%): Within healthy range (5-40%)
• ✅ DAG structure verified: Graph supports valid learning progressions
• ℹ️ Long dependency chains (20): Ensure students can follow extended learning paths
• ℹ️ Consider adding cross-dependencies: More connections could create richer learning pathways

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