Learning Graph Quality Metrics Report

Overview

• Total Concepts: 216
• Foundational Concepts (no prerequisites, other concepts depend on them): 3
• Terminal Nodes (nothing depends on them, but have prerequisites): 89
• Orphaned Nodes (completely disconnected, no edges): 0
• Concepts with Dependencies: 213
• Average Dependencies per Concept: 1.71

Graph Structure Validation

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

Foundational Concepts

These concepts have no prerequisites:

• 1: Business Purpose
• 2: Needs And Wants
• 3: Scarcity

Dependency Chain Analysis

• Maximum Dependency Chain Length: 16

Longest Learning Path:

1. Needs And Wants (ID: 2)
2. Goods And Services (ID: 5)
3. Market (ID: 14)
4. Competition (ID: 15)
5. Risk (ID: 16)
6. Decision Making (ID: 17)
7. PESTLE Analysis (ID: 21)
8. Strategic Analysis (ID: 55)
9. Case Study Analysis (ID: 199)
10. Evidence Based Judgment (ID: 200)
11. Research Ethics (ID: 209)
12. Internal Assessment (ID: 210)
13. Business Recommendation (ID: 211)
14. Evaluation Criteria (ID: 213)
15. Reflective Conclusion (ID: 214)
16. Presentation Of Findings (ID: 216)

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: 89 (41.2% of all concepts)
• Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

• 8: Added Value
• 23: Interest Rates
• 24: Inflation
• 29: Social Trends
• 31: Scenario Planning
• 34: Market Growth
• 36: Competitive Pressure
• 38: Intrapreneurship
• 40: Mission Statement
• 41: Vision Statement
• 43: Sole Proprietorship
• 44: Partnership
• 46: Franchise Model
• 47: Social Enterprise
• 48: Multinational Enterprise
• 49: Public Sector Organization
• 50: Private Sector Organization
• 52: Board Of Directors
• 53: Shareholder Value
• 57: SWOT Analysis

...and 69 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	17	Decision Making	16
2	13	Stakeholder	13
3	14	Market	11
4	16	Risk	11
5	10	Cost	9
6	73	Organizational Structure	9
7	42	Business Structure	8
8	127	Operations Management	7
9	145	Data Interpretation	7
10	1	Business Purpose	6

Outdegree Distribution

Dependencies	Number of Concepts
0	3
1	70
2	135
3	8

Recommendations

• ℹ️ High terminal node percentage (41.2%): Consider if some terminal concepts should be prerequisites for advanced concepts
• ✅ DAG structure verified: Graph supports valid learning progressions
• ℹ️ Long dependency chains (16): Ensure students can follow extended learning paths

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