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Learning Graph Quality Metrics Report

Overview

  • Total Concepts: 350
  • 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: 345
  • 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: 14

Longest Learning Path:

  1. Python Syntax (ID: 7)
  2. Variables (ID: 8)
  3. Data Types (ID: 9)
  4. Lists (ID: 14)
  5. Tuples (ID: 15)
  6. Time Tuple (ID: 86)
  7. Localtime Function (ID: 85)
  8. Utime Module (ID: 247)
  9. Ticks Ms Function (ID: 249)
  10. Ticks Diff Function (ID: 250)
  11. Elapsed Time Tracking (ID: 194)
  12. Timer (ID: 193)
  13. Countdown Timer (ID: 302)
  14. Pomodoro Timer (ID: 303)

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 (34.9% 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 57
4 6

Recommendations

  • ✅ Terminal node percentage (34.9%): Within healthy range (5-40%)
  • ✅ DAG structure verified: Graph supports valid learning progressions

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