Learning Graph Quality Metrics Report¶
Overview¶
- Total Concepts: 295
- Foundational Concepts (no prerequisites, other concepts depend on them): 1
- Terminal Nodes (nothing depends on them, but have prerequisites): 141
- Orphaned Nodes (completely disconnected, no edges): 0
- Concepts with Dependencies: 294
- Average Dependencies per Concept: 1.54
Graph Structure Validation¶
- Valid DAG Structure: ✅ Yes
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts¶
These concepts have no prerequisites:
- 1: English Language Arts Overview
Dependency Chain Analysis¶
- Maximum Dependency Chain Length: 13
Longest Learning Path:¶
- English Language Arts Overview (ID: 1)
- Literary Genres (ID: 15)
- Nonfiction (ID: 17)
- Informational Text (ID: 84)
- Rhetoric (ID: 89)
- Argument (ID: 90)
- Claims (ID: 91)
- Counterclaims (ID: 92)
- Argument Writing (ID: 122)
- Thesis Statement (ID: 136)
- Body Paragraph (ID: 138)
- Topic Sentence (ID: 140)
- Transitions (ID: 141)
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 (47.8% of all concepts)
- Healthy Range: 5-40% of total concepts
Concepts at the end of learning paths:
- 5: Grades 11-12 Standards Band
- 11: Lexile Level
- 12: Independent Reading
- 14: Domain-Specific Vocabulary
- 20: Short Story
- 21: Novel
- 22: Novella
- 23: Memoir
- 24: Essay
- 25: Epic Poetry
- 27: Comedy
- 28: Sonnet
- 29: Lyric Poetry
- 30: Free Verse
- 34: Protagonist and Antagonist
- 40: Resolution
- 41: Conflict Types
- 45: Unreliable Narrator
- 46: Cultural Perspective
- 48: Text Structure
...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 | 243 | Cognitive Bias | 17 |
| 2 | 8 | Close Reading | 15 |
| 3 | 1 | English Language Arts Overview | 13 |
| 4 | 84 | Informational Text | 13 |
| 5 | 221 | Critical Thinking | 11 |
| 6 | 104 | US Foundational Documents | 10 |
| 7 | 15 | Literary Genres | 9 |
| 8 | 49 | Figurative Language | 9 |
| 9 | 127 | Writing Process | 9 |
| 10 | 135 | Essay Structure | 9 |
Outdegree Distribution¶
| Dependencies | Number of Concepts |
|---|---|
| 0 | 1 |
| 1 | 151 |
| 2 | 128 |
| 3 | 15 |
Recommendations¶
- ℹ️ High terminal node percentage (47.8%): 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