Learning Graph Quality Metrics Report
Overview
- Total Concepts: 208
- Foundational Concepts (no prerequisites, other concepts depend on them): 11
- Terminal Nodes (nothing depends on them, but have prerequisites): 93
- Orphaned Nodes (completely disconnected, no edges): 0
- Concepts with Dependencies: 197
- Average Dependencies per Concept: 1.94
Graph Structure Validation
- Valid DAG Structure: ✅ Yes
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts
These concepts have no prerequisites:
- 1: Relation
- 12: Ordered Pair
- 14: X-Axis
- 15: Y-Axis
- 106: Base of an Exponential
- 159: Scale Factor
- 170: Coefficient
- 171: Variable
- 172: Constant
- 177: Number Systems
- 204: Significant Figures
Dependency Chain Analysis
- Maximum Dependency Chain Length: 11
Longest Learning Path:
- Relation (ID: 1)
- Function (ID: 2)
- Graph of a Function (ID: 18)
- Vertical Line Test (ID: 11)
- Horizontal Line Test (ID: 87)
- One-to-One Function (ID: 86)
- Inverse Function (ID: 82)
- Log-Exponential Inverse (ID: 121)
- Logarithmic Function (ID: 115)
- Logarithm Laws (ID: 118)
- Change of Base Rule (ID: 119)
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: 93 (44.7% of all concepts)
- Healthy Range: 5-40% of total concepts
Concepts at the end of learning paths:
- 8: Dependent Variable
- 9: Independent Variable
- 10: Mapping Diagram
- 21: Interval Notation
- 22: Set Builder Notation
- 25: Discrete Function
- 31: General Form of a Line
- 32: Point-Gradient Form
- 33: Gradient Calculation
- 34: Positive Gradient
- 35: Negative Gradient
- 36: Zero Gradient
- 37: Undefined Gradient
- 39: Perpendicular Lines
- 42: Intersection of Lines
- 43: Real-World Linear Models
- 45: Direct Proportion
- 47: Window Settings
- 48: Sketching vs Drawing
- 49: Key Graph Features
...and 73 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 | 18 | Graph of a Function | 34 |
| 2 | 2 | Function | 28 |
| 3 | 3 | Domain | 14 |
| 4 | 27 | Slope | 13 |
| 5 | 46 | Graphing Technology | 12 |
| 6 | 197 | Function Modeling | 11 |
| 7 | 125 | Polynomial Function | 10 |
| 8 | 62 | Quadratic Function | 7 |
| 9 | 105 | Exponential Function | 7 |
| 10 | 7 | Function Notation | 6 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 11 |
| 1 | 58 |
| 2 | 98 |
| 3 | 37 |
| 4 | 3 |
| 5 | 1 |
Recommendations
- ℹ️ High terminal node percentage (44.7%): 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