Learning Graph Quality Metrics Report
Overview
- Total Concepts: 200
- Foundational Concepts (no dependencies): 1
- Concepts with Dependencies: 199
- Average Dependencies per Concept: 1.68
Graph Structure Validation
- Valid DAG Structure: ❌ No
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts
These concepts have no prerequisites:
- 1: Scientific Reasoning
Dependency Chain Analysis
- Maximum Dependency Chain Length: 18
Longest Learning Path:
- Scientific Reasoning (ID: 1)
- Scientific Method (ID: 8)
- Evidence-Based Reasoning (ID: 9)
- Data Interpretation (ID: 10)
- Visual Data Representation (ID: 14)
- Graphs and Charts (ID: 33)
- Numerical Data Analysis (ID: 64)
- Data-Driven Reasoning (ID: 65)
- Logical Conclusions (ID: 66)
- Evaluating Scientific Claims (ID: 81)
- Evidence Supporting Conclusions (ID: 82)
- Conflicting Evidence (ID: 88)
- Data Consistency (ID: 90)
- Reproducibility (ID: 91)
- Peer Review Concepts (ID: 92)
- Scientific Consensus (ID: 93)
- Theory Modification (ID: 94)
- Paradigm Shifts (ID: 95)
Orphaned Nodes Analysis
- Total Orphaned Nodes: 69
Concepts that are not prerequisites for any other concept:
- 3: Career and College Readiness Standards
- 7: Test Item Alignment
- 16: Qualitative Reasoning
- 24: Restatements of Research
- 25: Scientific Comparisons
- 26: Scientific Processes
- 30: Scientific Symbols
- 32: Context Clues in Science
- 35: Data Visualization
- 37: Hypothesis Refinement
- 44: Error Reduction Strategies
- 45: Experimental Controls
- 49: Scientific Investigation Steps
- 52: Precision and Accuracy
- 53: Data Collection Methods
- 56: Comparing Experimental Designs
- 57: Observational Study Design
- 60: Confounding Variables
- 62: Citing Textual Evidence
- 63: Supporting Findings with Data
...and 49 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 | 18 | Experimental Design | 13 |
| 2 | 1 | Scientific Reasoning | 11 |
| 3 | 21 | Reading Scientific Text | 11 |
| 4 | 61 | Evidence-Based Conclusions | 7 |
| 5 | 141 | Descriptive Statistics | 7 |
| 6 | 161 | Human Body Systems | 7 |
| 7 | 8 | Scientific Method | 6 |
| 8 | 10 | Data Interpretation | 6 |
| 9 | 73 | Sampling Techniques | 6 |
| 10 | 81 | Evaluating Scientific Claims | 6 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 1 |
| 1 | 75 |
| 2 | 114 |
| 3 | 9 |
| 4 | 1 |
Recommendations
- ⚠️ Many orphaned nodes (69): Consider if these should be prerequisites for advanced concepts
- ℹ️ Long dependency chains (18): Ensure students can follow extended learning paths
Report generated by learning-graph-reports/analyze_graph.py