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Learning Graph Quality Metrics Report

Overview

  • Total Concepts: 297
  • Foundational Concepts (no prerequisites, other concepts depend on them): 2
  • Terminal Nodes (nothing depends on them, but have prerequisites): 105
  • Orphaned Nodes (completely disconnected, no edges): 0
  • Concepts with Dependencies: 295
  • Average Dependencies per Concept: 1.64

Graph Structure Validation

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

Foundational Concepts

These concepts have no prerequisites:

  • 1: Big Era Framework
  • 21: Big Bang

Dependency Chain Analysis

  • Maximum Dependency Chain Length: 56

Longest Learning Path:

  1. Big Bang (ID: 21)
  2. Cosmic Inflation (ID: 22)
  3. Formation Of Galaxies (ID: 24)
  4. Formation Of Solar System (ID: 25)
  5. Formation Of Earth (ID: 26)
  6. Geological Time Scale (ID: 27)
  7. Origin Of Life (ID: 28)
  8. Single-Celled Organisms (ID: 29)
  9. Photosynthesis Evolution (ID: 30)
  10. Cambrian Explosion (ID: 31)
  11. Mass Extinction Events (ID: 32)
  12. Mammalian Radiation (ID: 33)
  13. Primate Evolution (ID: 34)
  14. Hominin Evolution (ID: 35)
  15. Bipedalism (ID: 36)
  16. Australopithecus (ID: 37)
  17. Homo Habilis (ID: 38)
  18. Stone Tool Technology (ID: 40)
  19. Homo Erectus (ID: 39)
  20. Homo Sapiens Emergence (ID: 42)
  21. Hunter-Gatherer Societies (ID: 46)
  22. Band-Level Organization (ID: 47)
  23. Gender In Foraging Bands (ID: 70)
  24. Neolithic Revolution (ID: 71)
  25. Plant Domestication (ID: 72)
  26. Fertile Crescent (ID: 74)
  27. Wheat And Barley Origins (ID: 75)
  28. Sedentism (ID: 78)
  29. Neolithic Population Growth (ID: 83)
  30. Social Stratification (ID: 84)
  31. Surplus Food Production (ID: 85)
  32. Urban Revolution (ID: 88)
  33. Egyptian Civilization (ID: 99)
  34. Pyramid Construction (ID: 105)
  35. Old Kingdom Egypt (ID: 100)
  36. Middle Kingdom Egypt (ID: 101)
  37. New Kingdom Egypt (ID: 102)
  38. Late Bronze Age System (ID: 115)
  39. Late Bronze Age Collapse (ID: 122)
  40. Iron Age Transition (ID: 123)
  41. Iron Age (ID: 124)
  42. Axial Age (ID: 172)
  43. Hebrew Monotheism (ID: 177)
  44. Hebrew Prophets (ID: 178)
  45. Second Temple Judaism (ID: 179)
  46. Jesus Of Nazareth (ID: 148)
  47. Christianity Origins (ID: 147)
  48. Constantine Conversion (ID: 151)
  49. Late Antiquity (ID: 188)
  50. Western Christendom (ID: 220)
  51. Charlemagne (ID: 217)
  52. Carolingian Empire (ID: 216)
  53. Feudalism (ID: 218)
  54. Three-Field System (ID: 250)
  55. European Urban Revival (ID: 249)
  56. High Medieval Universities (ID: 251)

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: 105 (35.4% of all concepts)
  • Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

  • 3: Humans And Environment Theme
  • 4: Humans And Other Humans Theme
  • 5: Humans And Ideas Theme
  • 10: Historical Synthesis
  • 12: Historical Communication
  • 20: Historiography
  • 41: Control Of Fire
  • 55: Megafauna Extinctions
  • 58: Burial Practices
  • 59: Animism
  • 60: Language Evolution
  • 64: Denisovans
  • 65: Sapiens-Neanderthal Contact
  • 66: Microliths
  • 67: Coastal Migration Routes
  • 68: Ethnographic Analogy
  • 76: Rice Domestication
  • 80: Catalhoyuk
  • 81: Jericho
  • 82: Pottery Origins

...and 85 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 88 Urban Revolution 12
2 53 Ice Age Climate 9
3 44 Symbolic Thought 8
4 87 Metallurgy Origins 8
5 142 Roman Empire 8
6 147 Christianity Origins 8
7 89 Writing Systems 7
8 99 Egyptian Civilization 7
9 124 Iron Age 7
10 130 Achaemenid Empire 7

Outdegree Distribution

Dependencies Number of Concepts
0 2
1 131
2 146
3 14
4 3
6 1

Recommendations

  • ✅ Terminal node percentage (35.4%): Within healthy range (5-40%)
  • ✅ DAG structure verified: Graph supports valid learning progressions
  • ℹ️ Long dependency chains (56): Ensure students can follow extended learning paths

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