Learning Graph Quality Metrics Report
Overview
- Total Concepts: 300
- Foundational Concepts (no dependencies): 2
- Concepts with Dependencies: 298
- Average Dependencies per Concept: 1.69
Graph Structure Validation
- Valid DAG Structure: ❌ No
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts
These concepts have no prerequisites:
- 1: Statistics
- 148: Random Phenomenon
Dependency Chain Analysis
- Maximum Dependency Chain Length: 22
Longest Learning Path:
- Statistics (ID: 1)
- Data (ID: 2)
- Variable (ID: 3)
- Distribution (ID: 14)
- Center of Distribution (ID: 33)
- Mean (ID: 35)
- Standard Deviation (ID: 47)
- Variance (ID: 48)
- Variance of Random Variable (ID: 179)
- Standard Deviation of RV (ID: 180)
- SD of Sample Proportion (ID: 203)
- Standard Error (ID: 221)
- Margin of Error (ID: 216)
- Confidence Interval (ID: 215)
- Confidence Level (ID: 217)
- Critical Value (ID: 219)
- Z Critical Values (ID: 220)
- CI for One Proportion (ID: 222)
- Interpreting CI (ID: 224)
- Communicating Results (ID: 298)
- Four-Step Process (ID: 299)
- AP Exam Strategies (ID: 300)
Orphaned Nodes Analysis
- Total Orphaned Nodes: 108
Concepts that are not prerequisites for any other concept:
- 5: Dataset
- 9: Continuous Variable
- 17: Cumulative Frequency
- 18: Bar Graph
- 19: Pie Chart
- 20: Dotplot
- 21: Stemplot
- 23: Choosing Bin Width
- 26: Skewed Left
- 27: Skewed Right
- 28: Unimodal Distribution
- 29: Bimodal Distribution
- 30: Uniform Distribution
- 37: Mode
- 38: Resistant Measure
- 39: Comparing Mean and Median
- 45: Modified Boxplot
- 46: Comparing Distributions
- 49: Calculating Variance
- 55: Comparing with Z-Scores
...and 88 more
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 | 11 | Sample | 11 |
| 2 | 14 | Distribution | 10 |
| 3 | 24 | Shape of Distribution | 9 |
| 4 | 132 | Bias | 9 |
| 5 | 7 | Quantitative Variable | 8 |
| 6 | 35 | Mean | 8 |
| 7 | 56 | Normal Distribution | 7 |
| 8 | 110 | Experiment | 7 |
| 9 | 175 | Probability Distribution | 7 |
| 10 | 229 | Hypothesis Test | 7 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 2 |
| 1 | 129 |
| 2 | 140 |
| 3 | 22 |
| 4 | 6 |
| 5 | 1 |
Recommendations
- ⚠️ Many orphaned nodes (108): Consider if these should be prerequisites for advanced concepts
- ℹ️ Long dependency chains (22): Ensure students can follow extended learning paths
Report generated by learning-graph-reports/analyze_graph.py