Learning Graph Quality Metrics Report

Overview

• Total Concepts: 200
• Foundational Concepts (no prerequisites, other concepts depend on them): 3
• Terminal Nodes (nothing depends on them, but have prerequisites): 84
• Orphaned Nodes (completely disconnected, no edges): 0
• Concepts with Dependencies: 197
• Average Dependencies per Concept: 1.84

Graph Structure Validation

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

Foundational Concepts

These concepts have no prerequisites:

• 1: Enlightenment Philosophy
• 7: Articles of Confederation
• 191: Critical Thinking in Civics

Dependency Chain Analysis

• Maximum Dependency Chain Length: 15

Longest Learning Path:

1. Articles of Confederation (ID: 7)
2. Shays' Rebellion (ID: 8)
3. Constitutional Convention of 1787 (ID: 9)
4. Virginia Plan vs New Jersey Plan (ID: 10)
5. Great Compromise (ID: 11)
6. Bicameral Legislature (ID: 14)
7. Constitutional Structure (ID: 16)
8. Federal Court Structure (ID: 100)
9. District Courts (ID: 101)
10. Circuit Courts of Appeals (ID: 102)
11. Supreme Court (ID: 103)
12. Judicial Review (ID: 104)
13. Constitutional Interpretation (ID: 35)
14. Judicial Philosophy (ID: 108)
15. Judicial Restraint vs Activism (ID: 113)

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: 84 (42.0% of all concepts)
• Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

• 6: Declaration of Independence
• 20: Necessary and Proper Clause
• 21: Commerce Clause
• 22: Full Faith and Credit Clause
• 26: Second Amendment
• 33: Nineteenth Amendment
• 34: Twenty-Sixth Amendment
• 36: Originalism
• 37: Living Constitution Theory
• 41: Concurrent Powers
• 47: Block Grants
• 48: Unfunded Mandates
• 49: Nullification Doctrine
• 50: Preemption Doctrine
• 51: Devolution
• 55: Conference Committees
• 57: Speaker of the House
• 59: Cloture
• 61: Committee Markup
• 63: Pocket Veto

...and 64 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	16	Constitutional Structure	17
2	4	Popular Sovereignty	12
3	52	House of Representatives	12
4	53	Senate Structure	11
5	70	Enumerated Presidential Powers	11
6	86	Federal Bureaucracy Structure	9
7	140	Political Socialization	9
8	24	Bill of Rights	8
9	31	Fourteenth Amendment	8
10	38	Federalism	8

Outdegree Distribution

Dependencies	Number of Concepts
0	3
1	68
2	98
3	29
5	1
6	1

Recommendations

• ℹ️ High terminal node percentage (42.0%): Consider if some terminal concepts should be prerequisites for advanced concepts
• ✅ DAG structure verified: Graph supports valid learning progressions

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