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Learning Graph Quality Metrics Report

Overview

  • Total Concepts: 351
  • Foundational Concepts (no prerequisites, other concepts depend on them): 5
  • Terminal Nodes (nothing depends on them, but have prerequisites): 122
  • Orphaned Nodes (completely disconnected, no edges): 0
  • Concepts with Dependencies: 346
  • Average Dependencies per Concept: 1.90

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: Python Syntax
  • 39: Breadboard
  • 47: Microcontroller
  • 264: Ohms Law

Dependency Chain Analysis

  • Maximum Dependency Chain Length: 16

Longest Learning Path:

  1. Ohms Law (ID: 264)
  2. Voltage Levels (ID: 53)
  3. LED Basics (ID: 269)
  4. LED Display (ID: 123)
  5. Display Resolution (ID: 279)
  6. OLED Display (ID: 133)
  7. Framebuffer (ID: 138)
  8. Pixel Drawing (ID: 141)
  9. Line Drawing (ID: 142)
  10. Rectangle Drawing (ID: 143)
  11. Bounding Box (ID: 289)
  12. Clipping Region (ID: 290)
  13. Round Display (ID: 162)
  14. GC9A01 Driver (ID: 157)
  15. Smartwatch Display (ID: 163)
  16. Watch Band Integration (ID: 347)

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: 122 (34.8% of all concepts)
  • Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

  • 16: Dictionaries
  • 18: Assignment Operators
  • 23: Loop Control
  • 26: Lambda Functions
  • 31: Try Except Blocks
  • 38: Internal Pull-Up
  • 48: Physical Computing
  • 54: 3.3V vs 5V Logic
  • 55: Ground Connection
  • 61: I2C Pull-Up Resistors
  • 62: I2C Bus Speed
  • 66: SPI Chip Select
  • 67: SPI DC Pin
  • 68: SPI Reset Pin
  • 71: Bus Speed Comparison
  • 76: Hardware Debounce
  • 78: IRQ Falling Edge
  • 84: Encoder Acceleration
  • 90: Day of Year
  • 92: 24 Hour Format

...and 102 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 17 Arithmetic Operations 19
2 35 GPIO Pins 16
3 63 SPI Bus 14
4 56 I2C Bus 13
5 85 Localtime Function 13
6 264 Ohms Law 13
7 28 Libraries 12
8 6 MicroPython 11
9 47 Microcontroller 11
10 170 NeoPixel LEDs 11

Outdegree Distribution

Dependencies Number of Concepts
0 5
1 103
2 179
3 58
4 6

Recommendations

  • ✅ Terminal node percentage (34.8%): Within healthy range (5-40%)
  • ✅ DAG structure verified: Graph supports valid learning progressions
  • ℹ️ Long dependency chains (16): Ensure students can follow extended learning paths

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