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Learning Graph Quality Metrics Report

Overview

  • Total Concepts: 200
  • Foundational Concepts (no prerequisites, other concepts depend on them): 5
  • Terminal Nodes (nothing depends on them, but have prerequisites): 81
  • Orphaned Nodes (completely disconnected, no edges): 0
  • Concepts with Dependencies: 195
  • 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
  • 2: Decomposition
  • 3: Pattern Recognition
  • 4: Abstraction
  • 17: Scratch Editor

Dependency Chain Analysis

  • Maximum Dependency Chain Length: 12

Longest Learning Path:

  1. Scratch Editor (ID: 17)
  2. Sprite (ID: 19)
  3. X Coordinate (ID: 47)
  4. Y Coordinate (ID: 48)
  5. Coordinate Plane (ID: 49)
  6. Move Steps Block (ID: 55)
  7. Relative Movement (ID: 60)
  8. Drawing A Line (ID: 66)
  9. Drawing An Angle (ID: 67)
  10. Drawing A Polygon (ID: 68)
  11. Regular Polygon (ID: 73)
  12. Interior Angle (ID: 74)

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: 81 (40.5% of all concepts)
  • Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

  • 20: Sprite Costume
  • 21: Backdrop
  • 29: Looks Blocks
  • 30: Sound Blocks
  • 35: Program Flow
  • 59: Absolute Position
  • 62: Rotation Style
  • 65: Pen Trail
  • 69: Drawing A Triangle
  • 71: Drawing A Star
  • 74: Interior Angle
  • 75: Exterior Angle
  • 77: Pen Size
  • 78: Stamp Block
  • 79: Clear Block
  • 80: Generative Art Pattern
  • 87: Loop Counter
  • 88: Nested Loop
  • 89: Loop Body
  • 90: Exiting A Loop

...and 61 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 24 Block Categories 8
2 68 Drawing A Polygon 8
3 96 Creating A Variable 8
4 34 Sequencing 7
5 81 Loop 7
6 1 Computational Thinking 6
7 26 Pen Blocks 6
8 83 Fixed-Count Loop 6
9 183 Turtle Module 6
10 6 Algorithm 5

Outdegree Distribution

Dependencies Number of Concepts
0 5
1 133
2 53
3 8
4 1

Recommendations

  • ℹ️ High terminal node percentage (40.5%): Consider if some terminal concepts should be prerequisites for advanced concepts
  • ✅ DAG structure verified: Graph supports valid learning progressions
  • ℹ️ Consider adding cross-dependencies: More connections could create richer learning pathways

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