Learning Graph Quality Metrics Report

Overview

• Total Concepts: 450
• Foundational Concepts (no prerequisites, other concepts depend on them): 2
• Terminal Nodes (nothing depends on them, but have prerequisites): 131
• Orphaned Nodes (completely disconnected, no edges): 0
• Concepts with Dependencies: 448
• Average Dependencies per Concept: 1.72

Graph Structure Validation

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

Foundational Concepts

These concepts have no prerequisites:

• 1: Pre-Columbian Civilizations
• 375: Historical Causation

Dependency Chain Analysis

• Maximum Dependency Chain Length: 94

Longest Learning Path:

1. Pre-Columbian Civilizations (ID: 1)
2. European Exploration Motives (ID: 7)
3. Christopher Columbus (ID: 8)
4. Columbian Exchange (ID: 10)
5. Disease and Indigenous Depopulation (ID: 11)
6. Encomienda System (ID: 16)
7. Atlantic Slave Trade Origins (ID: 17)
8. Slavery in the Colonies (ID: 30)
9. Triangular Trade (ID: 31)
10. Mercantilism (ID: 32)
11. Navigation Acts (ID: 33)
12. Stamp Act (ID: 48)
13. Townshend Acts (ID: 49)
14. Boston Tea Party (ID: 51)
15. Intolerable Acts (ID: 52)
16. First Continental Congress (ID: 53)
17. Lexington and Concord (ID: 54)
18. Second Continental Congress (ID: 55)
19. Common Sense (Paine) (ID: 56)
20. Declaration of Independence (ID: 57)
21. Treaty of Paris 1783 (ID: 62)
22. Articles of Confederation (ID: 63)
23. Shays' Rebellion (ID: 64)
24. Constitutional Convention (ID: 65)
25. George Washington as President (ID: 72)
26. Washington's Farewell Address (ID: 76)
27. John Adams Presidency (ID: 77)
28. XYZ Affair (ID: 78)
29. Alien and Sedition Acts (ID: 79)
30. Election of 1800 (ID: 81)
31. Jeffersonian Democracy (ID: 82)
32. War of 1812 (ID: 87)
33. Era of Good Feelings (ID: 88)
34. Manifest Destiny (ID: 98)
35. Transcontinental Railroad (ID: 146)
36. Railroad Expansion (ID: 147)
37. Rise of Big Business (ID: 148)
38. Robber Barons (ID: 149)
39. Gilded Age Politics (ID: 174)
40. Progressive Era (ID: 182)
41. Square Deal (ID: 188)
42. Theodore Roosevelt (ID: 187)
43. Woodrow Wilson (ID: 208)
44. World War I Causes (ID: 209)
45. Zimmermann Telegram (ID: 210)
46. U.S. Entry into WWI (ID: 211)
47. Fourteen Points (ID: 216)
48. Treaty of Versailles (ID: 217)
49. Consumer Culture of 1920s (ID: 221)
50. 1929 Stock Market Crash (ID: 234)
51. Causes of the Great Depression (ID: 235)
52. Bank Failures (ID: 236)
53. Herbert Hoover's Response (ID: 237)
54. Bonus Army (ID: 239)
55. Franklin D. Roosevelt (ID: 240)
56. Lend-Lease Act (ID: 254)
57. U.S. Entry into WWII (ID: 256)
58. Manhattan Project (ID: 264)
59. Atomic Bombs on Japan (ID: 265)
60. Yalta Conference (ID: 267)
61. United Nations Formation (ID: 268)
62. Origins of the Cold War (ID: 269)
63. Containment Policy (ID: 270)
64. Truman Doctrine (ID: 271)
65. Korean War (ID: 275)
66. McCarthyism (ID: 276)
67. Brown v. Board of Education (ID: 283)
68. Montgomery Bus Boycott (ID: 284)
69. Student Nonviolent Coordinating Committee (ID: 288)
70. Sit-In Movement (ID: 289)
71. Freedom Riders (ID: 290)
72. Birmingham Campaign (ID: 291)
73. March on Washington (ID: 292)
74. Civil Rights Act of 1964 (ID: 293)
75. Lyndon B. Johnson (ID: 300)
76. Gulf of Tonkin Resolution (ID: 301)
77. Vietnam War Escalation (ID: 302)
78. Tet Offensive (ID: 303)
79. Anti-War Movement (ID: 304)
80. Kent State Shooting (ID: 305)
81. Nixon and Détente (ID: 307)
82. Watergate Scandal (ID: 308)
83. Ford and Carter Administrations (ID: 316)
84. Iranian Hostage Crisis (ID: 318)
85. Reagan Revolution (ID: 319)
86. Cold War End (ID: 322)
87. Gorbachev and Glasnost (ID: 323)
88. Fall of Berlin Wall (ID: 324)
89. Dissolution of Soviet Union (ID: 325)
90. Gulf War 1991 (ID: 326)
91. 9/11 Attacks (ID: 330)
92. War on Terror (ID: 331)
93. Iraq War 2003 (ID: 333)
94. Hurricane Katrina Response (ID: 334)

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: 131 (29.1% of all concepts)
• Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

• 5: Mississippian Culture
• 6: Iroquois Confederacy
• 13: Dutch Exploration
• 15: Treaty of Tordesillas
• 19: John Smith
• 20: Powhatan Confederacy
• 26: Roger Williams and Rhode Island
• 27: Anne Hutchinson
• 34: Bacon's Rebellion
• 35: Salem Witch Trials
• 37: Town Meetings
• 38: House of Burgesses
• 40: Jonathan Edwards
• 41: Colonial Social Structure
• 42: Plantation Economy
• 43: Middle Passage
• 50: Boston Massacre
• 61: Marquis de Lafayette
• 67: Three-Fifths Compromise
• 103: Frederick Douglass

...and 111 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	182	Progressive Era	14
2	30	Slavery in the Colonies	13
3	68	Federalism	13
4	2	Indigenous North American Cultures	11
5	65	Constitutional Convention	11
6	293	Civil Rights Act of 1964	11
7	71	Bill of Rights	8
8	102	Abolitionism	8
9	109	Industrial Revolution in America	8
10	148	Rise of Big Business	8

Outdegree Distribution

Dependencies	Number of Concepts
0	2
1	160
2	254
3	34

Recommendations

• ✅ Terminal node percentage (29.1%): Within healthy range (5-40%)
• ✅ DAG structure verified: Graph supports valid learning progressions
• ℹ️ Long dependency chains (94): Ensure students can follow extended learning paths

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