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Learning Graph Quality Metrics Report

Overview

  • Total Concepts: 400
  • Foundational Concepts (no prerequisites, other concepts depend on them): 24
  • Terminal Nodes (nothing depends on them, but have prerequisites): 172
  • Orphaned Nodes (completely disconnected, no edges): 0
  • Concepts with Dependencies: 376
  • Average Dependencies per Concept: 1.78

Graph Structure Validation

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

Foundational Concepts

These concepts have no prerequisites:

  • 1: Moss Definition
  • 6: Vascular Plants
  • 7: Plant Evolution
  • 67: Ecosystem Services
  • 87: Carbon Cycle
  • 122: Climate Zones
  • 213: Building Envelope
  • 268: Air Circulation
  • 296: Feedback Loops
  • 297: Emergent Properties
  • 307: Scientific Method Review
  • 317: Machine Learning Basics
  • 346: Scientific Observation
  • 348: Lab Safety
  • 354: Technical Writing
  • 355: Collaborative Learning
  • 357: Design Thinking
  • 360: Critical Thinking
  • 372: Soil Science Basics
  • 373: pH and Chemistry Basics
  • 374: Light and Energy Basics
  • 375: Water Cycle Basics
  • 384: Cell Biology Basics
  • 389: Natural Selection

Dependency Chain Analysis

  • Maximum Dependency Chain Length: 13

Longest Learning Path:

  1. Moss Definition (ID: 1)
  2. Bryophytes (ID: 2)
  3. Moss Diversity (ID: 9)
  4. Moss Growth Forms (ID: 58)
  5. Moss Texture (ID: 65)
  6. Moss Aesthetic Qualities (ID: 116)
  7. Moss Garden Benefits (ID: 112)
  8. Mossarium Definition (ID: 150)
  9. Nature Connection Indoors (ID: 183)
  10. Biophilic Design (ID: 179)
  11. Healing Gardens (ID: 234)
  12. Contemplative Gardens (ID: 232)
  13. Sacred Groves (ID: 233)

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: 172 (43.0% of all concepts)
  • Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

  • 3: Liverworts
  • 4: Hornworts
  • 11: Moss vs Ferns
  • 12: Moss vs Grass
  • 13: Moss vs Succulents
  • 21: Alternation of Generations
  • 22: Rhizoids
  • 23: Moss Leaves
  • 24: Moss Stems
  • 26: Seta
  • 27: Calyptra
  • 29: Spore Dispersal
  • 30: Spores vs Seeds
  • 31: Water in Fertilization
  • 33: Protonema
  • 37: Chloroplasts in Moss
  • 39: Sheet Moss
  • 40: Cushion Moss
  • 41: Haircap Moss
  • 42: Rock Cap Moss

...and 152 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 1 Moss Definition 63
2 66 Moss Ecology 26
3 112 Moss Garden Benefits 16
4 150 Mossarium Definition 12
5 2 Bryophytes 9
6 214 Moss Art Overview 9
7 272 Moss in K-12 Education 9
8 6 Vascular Plants 8
9 240 Moss Propagation 8
10 292 Systems Thinking 8

Outdegree Distribution

Dependencies Number of Concepts
0 24
1 110
2 241
3 22
4 2
5 1

Recommendations

  • ℹ️ High terminal node percentage (43.0%): Consider if some terminal concepts should be prerequisites for advanced concepts
  • ✅ DAG structure verified: Graph supports valid learning progressions

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