Learning Graph Quality Metrics Report¶
Overview¶
- Total Concepts: 581
- Foundational Concepts (no prerequisites, other concepts depend on them): 3
- Terminal Nodes (nothing depends on them, but have prerequisites): 188
- Orphaned Nodes (completely disconnected, no edges): 0
- Concepts with Dependencies: 578
- Average Dependencies per Concept: 1.90
Graph Structure Validation¶
- Valid DAG Structure: ✅ Yes
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts¶
These concepts have no prerequisites:
- 1: Air Movement
- 2: Fan Speed
- 3: Horsepower
Dependency Chain Analysis¶
- Maximum Dependency Chain Length: 18
Longest Learning Path:¶
- Air Movement (ID: 1)
- Fan (ID: 25)
- Impeller (ID: 28)
- Fan Shaft (ID: 31)
- Bearing (ID: 32)
- Drive Train (ID: 34)
- Belt Drive (ID: 134)
- Fan Arrangement (ID: 141)
- Viewed From Drive Side (ID: 161)
- Rotation (ID: 162)
- Clockwise Rotation (ID: 163)
- Rotation and Discharge Code (ID: 173)
- Complete Fan Description (ID: 385)
- Fan Specification (ID: 386)
- CSI Format Specification (ID: 577)
- Specification Performance Clause (ID: 578)
- Specification Review (ID: 387)
- Capstone Fan Specification (ID: 390)
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: 188 (32.4% of all concepts)
- Healthy Range: 5-40% of total concepts
Concepts at the end of learning paths:
- 51: Ring Fan
- 56: Filtered Supply Fan
- 60: Centrifugal Wall Exhauster
- 61: Roof Mounted Axial Fan
- 62: Wall Mounted Fan
- 63: Gravity Relief Ventilator
- 65: Cabinet Ventilator
- 71: Mancooler
- 79: Nozzle and Windband
- 83: Scroll Wrapper
- 90: Belt Tube
- 93: Bolted Housing
- 100: Horizontal Split Housing
- 101: Three-Way Split Housing
- 102: Pie Split Housing
- 104: Blade Leading Edge
- 121: Fixed Pitch Impeller
- 127: Reversible Impeller
- 130: Reverse Bore Hub
- 131: Back Plate Fins
...and 168 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 | 32 | Bearing | 24 |
| 2 | 28 | Impeller | 21 |
| 3 | 33 | Fan Motor | 19 |
| 4 | 31 | Fan Shaft | 18 |
| 5 | 30 | Fan Outlet | 16 |
| 6 | 27 | Fan Housing | 14 |
| 7 | 37 | Axial Fan | 14 |
| 8 | 29 | Fan Inlet | 13 |
| 9 | 141 | Fan Arrangement | 13 |
| 10 | 35 | Fan Family | 11 |
Outdegree Distribution¶
| Dependencies | Number of Concepts |
|---|---|
| 0 | 3 |
| 1 | 236 |
| 2 | 252 |
| 3 | 61 |
| 4 | 13 |
| 5 | 1 |
| 6 | 5 |
| 7 | 4 |
| 8 | 2 |
| 9 | 1 |
| 10 | 1 |
| 11 | 1 |
| 14 | 1 |
Recommendations¶
- ✅ Terminal node percentage (32.4%): Within healthy range (5-40%)
- ✅ DAG structure verified: Graph supports valid learning progressions
- ℹ️ Long dependency chains (18): Ensure students can follow extended learning paths
Report generated by learning-graph-reports/analyze_graph.py