Learning Graph Quality Metrics Report¶
Overview¶
- Total Concepts: 200
- Foundational Concepts (no prerequisites, other concepts depend on them): 7
- Terminal Nodes (nothing depends on them, but have prerequisites): 81
- Orphaned Nodes (completely disconnected, no edges): 0
- Concepts with Dependencies: 193
- Average Dependencies per Concept: 1.67
Graph Structure Validation¶
- Valid DAG Structure: ✅ Yes
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts¶
These concepts have no prerequisites:
- 1: Entrepreneurship
- 2: Liberal Arts Education
- 3: Creativity
- 7: Growth Mindset
- 12: Curiosity
- 14: Communication Skills
- 195: Ole Cup Timeline
Dependency Chain Analysis¶
- Maximum Dependency Chain Length: 16
Longest Learning Path:¶
- Creativity (ID: 3)
- Problem Solving (ID: 5)
- Design Thinking (ID: 35)
- User Empathy Mapping (ID: 36)
- Customer Pain Points (ID: 52)
- Problem-Solution Fit (ID: 64)
- Value Proposition (ID: 66)
- Competitive Differentiation (ID: 77)
- Unique Selling Proposition (ID: 78)
- Brand Identity (ID: 158)
- Brand Story (ID: 159)
- Pitch Story Arc (ID: 170)
- Pitch Deck (ID: 176)
- Pitch Delivery (ID: 187)
- Q&A Handling (ID: 188)
- Live Pitch (ID: 191)
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: 81 (40.5% of all concepts)
- Healthy Range: 5-40% of total concepts
Concepts at the end of learning paths:
- 4: Innovation
- 9: Resilience
- 11: Motivation
- 26: Ikigai Venn Diagram
- 34: SCAMPER Method
- 37: Random Association Technique
- 38: Problem Inversion
- 40: Music as Idea Source
- 41: Visual Arts as Idea Source
- 42: Theater as Idea Source
- 43: Science as Idea Source
- 44: Humanities as Idea Source
- 46: Idea Capture
- 48: Convergent Thinking
- 50: Liberal Arts Advantage
- 53: Underserved Markets
- 54: Social Gaps
- 56: Demographic Shifts
- 57: Technology Waves
- 58: Cultural Movements
...and 61 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 | 176 | Pitch Deck | 10 |
| 2 | 1 | Entrepreneurship | 9 |
| 3 | 31 | Ideation | 9 |
| 4 | 68 | Customer Segments | 9 |
| 5 | 128 | Business Model Canvas | 8 |
| 6 | 2 | Liberal Arts Education | 7 |
| 7 | 13 | Ethical Reasoning | 7 |
| 8 | 14 | Communication Skills | 7 |
| 9 | 66 | Value Proposition | 7 |
| 10 | 3 | Creativity | 6 |
Outdegree Distribution¶
| Dependencies | Number of Concepts |
|---|---|
| 0 | 7 |
| 1 | 78 |
| 2 | 104 |
| 3 | 9 |
| 4 | 1 |
| 5 | 1 |
Recommendations¶
- ℹ️ High terminal node percentage (40.5%): 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
Report generated by learning-graph-reports/analyze_graph.py