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Learning Graph Quality Metrics Report

Overall Quality Score: 93/100

Rating: Excellent — this graph is ready to drive chapter design.

This score is an editorial judgment layered on top of the automated metrics below (produced by analyze-graph.py), which check DAG validity, connectivity, and degree distributions but do not themselves compute a single score.

What earns the high score:

  • Valid DAG, zero cycles, zero self-dependencies — the graph is structurally sound.
  • Fully connected: 1 connected component across all 293 concepts, 0 orphaned nodes (after two rounds of fixes — see below).
  • Healthy foundational base: 14 zero-dependency concepts anchor the graph, spanning hardware (breadboard, buttons, potentiometer, rotary encoder, SPI/I2C interfaces), software fundamentals (comment syntax, indentation), and the two non-technical research anchors (Ekman's universal emotions, computational thinking, screen-based robot face) that let history/psychology content stand on its own rather than forcing artificial technical prerequisites onto it.
  • Healthy terminal-node ratio: 34.5% (101 of 293) — comfortably inside the 5-40% healthy range. Terminal nodes cluster sensibly at true endpoints: capstone deliverables (Capstone Demonstration, Original Robot Personality), business/history conclusions (Robot Business Case Study, Educational Robotics Market), and specialized wiring details (Display Mounting Considerations).
  • Genuine multi-path structure, not a linear chain: average outdegree 1.82, with 154 concepts (52.6%) drawing on 2 prerequisites and 30 concepts drawing on 3-6, meaning most concepts converge from multiple prior ideas rather than following one single-file thread. High-indegree hubs (Frame Buffer: 13, Ellipse Method: 12, Neutral Expression: 12, Face Outline: 10) are exactly the concepts that should be hubs pedagogically — they are reused across drawing, anatomy, emotion, and history branches.
  • The longest path (27 concepts, Microcontroller -> ... -> Capstone Demonstration) is plausible for a course that starts at bare-metal hardware and ends at a two-display capstone; it is not a sign of an artificially stretched chain, since 96 other concepts also reach the graph's terminal layer by other, shorter paths.

What holds it back from higher:

  • The single longest chain (27 hops) is long enough that a strictly linear reading of it would be taxing; students should be encouraged to use the graph's many shorter alternate paths rather than the single deepest one.
  • A handful of small clusters (e.g., the rotary-encoder sub-cluster) needed an explicit cross-link (into Live Parameter Tuning / Control Mapping Design) to avoid becoming an isolated island. This was fixed, but it is a reminder that peripheral hardware topics need deliberate integration back into the main line of the course.
  • 101 terminal nodes is on the higher side of "healthy," reflecting how many distinct, specific concepts (individual emotions, individual robots, individual wiring pins) exist in this domain; this is appropriate for the subject matter rather than a defect, but chapter design should group these into coherent clusters rather than treating each as an independent lesson.

Overview

  • Total Concepts: 293
  • Foundational Concepts (no prerequisites, other concepts depend on them): 14
  • Terminal Nodes (nothing depends on them, but have prerequisites): 101
  • Orphaned Nodes (completely disconnected, no edges): 0
  • Concepts with Dependencies: 279
  • Average Dependencies per Concept: 1.82

Graph Structure Validation

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

Foundational Concepts

These concepts have no prerequisites:

  • 3: Microcontroller
  • 5: Solderless Breadboard
  • 6: Jumper Wires
  • 7: Momentary Push Button
  • 8: Potentiometer
  • 9: Rotary Encoder
  • 10: SPI Interface
  • 11: I2C Interface
  • 26: Screen-Based Robot Face
  • 70: Comment Syntax
  • 71: Indentation Rules
  • 84: Pixel
  • 170: Ekman Universal Emotions
  • 271: Computational Thinking

Dependency Chain Analysis

  • Maximum Dependency Chain Length: 27

Longest Learning Path:

  1. Microcontroller (ID: 3)
  2. RP2040 Microcontroller (ID: 2)
  3. Raspberry Pi Pico (ID: 1)
  4. MicroPython (ID: 51)
  5. Module (ID: 66)
  6. Import Statement (ID: 65)
  7. FrameBuf Module (ID: 74)
  8. Frame Buffer (ID: 85)
  9. Horizontal Line Method (ID: 100)
  10. Rectangle Method (ID: 103)
  11. Ellipse Method (ID: 120)
  12. Face Outline (ID: 147)
  13. Eye Placement (ID: 148)
  14. Eye Size Parameter (ID: 149)
  15. Pupil (ID: 151)
  16. Draw Face Function (ID: 161)
  17. Animation Loop (ID: 203)
  18. Timing Loop (ID: 208)
  19. Sleep Function Timing (ID: 209)
  20. Ticks Function Timing (ID: 214)
  21. Ticks Diff Calculation (ID: 215)
  22. Draw Time Benchmarking (ID: 216)
  23. Expressiveness Versus Complexity (ID: 280)
  24. Constraint-Driven Design (ID: 286)
  25. Minimum Viable Feature Set (ID: 287)
  26. Capstone Project (ID: 288)
  27. Capstone Demonstration (ID: 289)

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: 101 (34.5% of all concepts)
  • Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

  • 4: Cytron Maker Pi RP2040
  • 15: Data Command Pin
  • 21: Pull-Up Resistor
  • 23: Breadboard Wiring Diagram
  • 24: Display Power Requirements
  • 25: Display Mounting Considerations
  • 40: Robot Face Design Scoping
  • 43: Robot Voice Interaction
  • 44: Robot Business Case Study
  • 46: Anki Company History
  • 48: Robot Personality Branding
  • 49: Screen As Face Metaphor
  • 50: Educational Robotics Market
  • 62: For Loop
  • 73: Bit Shifting
  • 75: String Formatting
  • 77: Multiple Return Values
  • 93: Bounding Box
  • 95: Show Method
  • 96: Frame Buffer Size Calculation

...and 81 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 85 Frame Buffer 13
2 120 Ellipse Method 12
3 175 Neutral Expression 12
4 147 Face Outline 10
5 153 Eyebrow Shape 9
6 155 Mouth Shape 9
7 203 Animation Loop 9
8 10 SPI Interface 8
9 250 RGB565 Color Model 8
10 54 Variable 7

Outdegree Distribution

Dependencies Number of Concepts
0 14
1 95
2 154
3 21
4 4
5 3
6 2

Recommendations

  • ✅ Terminal node percentage (34.5%): Within healthy range (5-40%)
  • ✅ DAG structure verified: Graph supports valid learning progressions
  • ℹ️ Long dependency chains (27): Ensure students can follow extended learning paths

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