Learning Graph Quality Metrics Report

Overview

• Total Concepts: 537
• Foundational Concepts (no prerequisites, other concepts depend on them): 6
• Terminal Nodes (nothing depends on them, but have prerequisites): 159
• Orphaned Nodes (completely disconnected, no edges): 0
• Concepts with Dependencies: 531
• Average Dependencies per Concept: 1.71

Graph Structure Validation

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

Foundational Concepts

These concepts have no prerequisites:

• 1: Learning Python Prerequisites
• 26: Robot Arm
• 120: Voltage
• 194: 3D Printing
• 364: Camera
• 396: Large Language Model

Dependency Chain Analysis

• Maximum Dependency Chain Length: 22

Longest Learning Path:

1. Voltage (ID: 120)
2. Serial Communication (ID: 87)
3. UART (ID: 88)
4. USB Serial Adapter (ID: 91)
5. Serial Port (ID: 92)
6. Pyserial Library (ID: 93)
7. Reading a Register (ID: 114)
8. Reading Joint Positions (ID: 280)
9. Raw Servo Units (ID: 282)
10. Unit Conversion (ID: 284)
11. Joint-Space Motion (ID: 285)
12. Single-Joint Move (ID: 286)
13. Multi-Joint Move (ID: 287)
14. Waypoint List (ID: 289)
15. Pick and Place (ID: 306)
16. Task Planning (ID: 436)
17. Agent Planner (ID: 421)
18. Learned Policy Executor (ID: 422)
19. Planner-Executor Split (ID: 423)
20. Desk Assistant Project (ID: 462)
21. Capstone Project (ID: 466)
22. Project Documentation (ID: 467)

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: 159 (29.6% of all concepts)
• Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

• 3: REPL
• 8: Requirements File
• 15: Naming Conventions
• 19: Code Editor
• 21: Configuration File
• 23: Argparse Module
• 30: Prismatic Joint
• 40: Accuracy
• 43: Shoulder
• 59: Hobby Servo
• 74: Magnetic Encoder
• 76: Velocity Feedback
• 82: Overload Protection
• 84: Servo Compliance
• 85: Quasi-Direct Drive
• 86: Motor Controller
• 101: Daisy Chain Wiring
• 104: CAN Frame
• 109: Vendor SDK
• 110: Struct Module

...and 139 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	142	Robot Safety	16
2	4	Python Script	15
3	26	Robot Arm	14
4	1	Learning Python Prerequisites	13
5	57	Actuator	12
6	120	Voltage	11
7	398	Agent Tool	11
8	7	Pip	10
9	28	Joint	10
10	162	Bill of Materials	9

Outdegree Distribution

Dependencies	Number of Concepts
0	6
1	207
2	272
3	51
4	1

Recommendations

• ✅ Terminal node percentage (29.6%): Within healthy range (5-40%)
• ✅ DAG structure verified: Graph supports valid learning progressions
• ℹ️ Long dependency chains (22): Ensure students can follow extended learning paths

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