Learning Graph Quality Metrics Report¶
Overview¶
- Total Concepts: 292
- Foundational Concepts (no prerequisites, other concepts depend on them): 12
- Terminal Nodes (nothing depends on them, but have prerequisites): 141
- Orphaned Nodes (completely disconnected, no edges): 0
- Concepts with Dependencies: 280
- Average Dependencies per Concept: 1.66
Graph Structure Validation¶
- Valid DAG Structure: ✅ Yes
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts¶
These concepts have no prerequisites:
- 1: Algebra Basics
- 2: Geometry Basics
- 3: Units And Measurement
- 4: Computer File Management
- 5: Mouse And 3D Navigation
- 6: Basic Physics Concepts
- 9: Industrial Revolution
- 19: ISO Standards Body
- 20: ASTM International
- 44: PLTW Design Process
- 194: Workshop Safety
- 201: Intellectual Property
Dependency Chain Analysis¶
- Maximum Dependency Chain Length: 14
Longest Learning Path:¶
- Industrial Revolution (ID: 9)
- Subtractive Manufacturing (ID: 10)
- Additive Manufacturing (ID: 11)
- ISO ASTM 52900 Standard (ID: 21)
- AM Process Categories (ID: 22)
- Material Extrusion (ID: 29)
- FDM FFF Process (ID: 36)
- FDM Printer Anatomy (ID: 103)
- Stepper Motors (ID: 109)
- Belts And Pulleys (ID: 110)
- Ringing And Ghosting (ID: 183)
- Input Shaping (ID: 235)
- High-Speed Printing (ID: 237)
- High-Flow Hotend (ID: 240)
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: 141 (48.3% of all concepts)
- Healthy Range: 5-40% of total concepts
Concepts at the end of learning paths:
- 7: Mass And Density
- 12: Stereolithography Invention
- 17: AM Innovation Institutes
- 18: Maker Movement
- 23: AM Vocabulary Glossary
- 32: Material Jetting
- 33: Binder Jetting
- 34: Directed Energy Deposition
- 35: Sheet Lamination
- 39: DLP Process
- 40: SLS Process
- 41: MJF Process
- 46: Research Phase
- 49: Concept Selection
- 52: Testing And Validation
- 61: Extrude Feature
- 62: Revolve Feature
- 63: Sweep And Loft
- 64: Fillet And Chamfer
- 65: Shell Feature
...and 121 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 | 122 | Thermoplastics | 19 |
| 2 | 83 | Slicer Software | 18 |
| 3 | 11 | Additive Manufacturing | 13 |
| 4 | 24 | Layer-By-Layer Principle | 13 |
| 5 | 126 | Material Data Sheet | 12 |
| 6 | 175 | Troubleshooting Workflow | 12 |
| 7 | 36 | FDM FFF Process | 10 |
| 8 | 60 | Feature-Based Modeling | 10 |
| 9 | 136 | Photopolymer Resins | 10 |
| 10 | 155 | DfAM Principles | 10 |
Outdegree Distribution¶
| Dependencies | Number of Concepts |
|---|---|
| 0 | 12 |
| 1 | 130 |
| 2 | 121 |
| 3 | 24 |
| 4 | 5 |
Recommendations¶
- ℹ️ High terminal node percentage (48.3%): Consider if some terminal concepts should be prerequisites for advanced concepts
- ✅ DAG structure verified: Graph supports valid learning progressions
Report generated by learning-graph-reports/analyze_graph.py