Skip to content

Learning Graph Quality Metrics Report

Overview

  • Total Concepts: 380
  • Foundational Concepts (no prerequisites, other concepts depend on them): 6
  • Terminal Nodes (nothing depends on them, but have prerequisites): 181
  • Orphaned Nodes (completely disconnected, no edges): 0
  • Concepts with Dependencies: 374
  • Average Dependencies per Concept: 1.63

Graph Structure Validation

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

Foundational Concepts

These concepts have no prerequisites:

  • 1: Ecology
  • 13: Energy
  • 14: Matter
  • 151: Plate Tectonics
  • 312: System
  • 342: Hypothesis

Dependency Chain Analysis

  • Maximum Dependency Chain Length: 11

Longest Learning Path:

  1. Matter (ID: 14)
  2. Nutrients (ID: 15)
  3. Biogeochemical Cycles (ID: 61)
  4. Carbon Cycle (ID: 62)
  5. Carbon Dioxide (ID: 70)
  6. Greenhouse Effect (ID: 285)
  7. Greenhouse Gases (ID: 286)
  8. Global Climate Change (ID: 287)
  9. Ocean Warming (ID: 290)
  10. ENSO Cycle (ID: 174)
  11. El Nino (ID: 172)

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: 181 (47.6% of all concepts)
  • Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

  • 11: Biosphere
  • 18: Organic Molecules
  • 19: Inorganic Molecules
  • 22: Tropical Rainforest
  • 23: Temperate Forest
  • 24: Desert Biome
  • 25: Tundra Biome
  • 26: Grassland Biome
  • 27: Chaparral Biome
  • 28: Taiga Biome
  • 31: Rivers and Streams
  • 32: Lakes and Ponds
  • 34: Estuaries
  • 45: Energy Pyramids
  • 52: Autotrophs
  • 53: Heterotrophs
  • 54: Chemosynthesis
  • 56: Entropy in Ecosystems
  • 58: Energy Loss as Heat
  • 59: Trophic Efficiency

...and 161 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 7 Population 21
2 201 Sustainability 16
3 6 Species 15
4 13 Energy 15
5 236 Air Pollution 12
6 2 Ecosystem 11
7 5 Biodiversity 11
8 287 Global Climate Change 11
9 312 System 9
10 314 Feedback Loops 9

Outdegree Distribution

Dependencies Number of Concepts
0 6
1 162
2 190
3 21
4 1

Recommendations

  • ℹ️ High terminal node percentage (47.6%): 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