Learning Graph Quality Metrics Report¶
Overview¶
- Total Concepts: 195
- Foundational Concepts (no dependencies): 2
- Concepts with Dependencies: 193
- Average Dependencies per Concept: 1.37
Graph Structure Validation¶
- Valid DAG Structure: ❌ No
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts¶
These concepts have no prerequisites:
- 1: Spoken Language
- 161: Repetition
Dependency Chain Analysis¶
- Maximum Dependency Chain Length: 26
Longest Learning Path:¶
- Spoken Language (ID: 1)
- Listening Skills (ID: 2)
- Sounds in Environment (ID: 3)
- Speech Sounds (ID: 4)
- Words (ID: 5)
- Phoneme (ID: 6)
- Phonemic Awareness (ID: 68)
- Initial Sound (ID: 69)
- Final Sound (ID: 70)
- Medial Sound (ID: 71)
- Sound Isolation (ID: 72)
- Sound Segmentation (ID: 73)
- Sound Blending (ID: 126)
- Oral Blending (ID: 127)
- Continuous Blending (ID: 128)
- Blending VC Words (ID: 131)
- Blending CVC Words (ID: 132)
- Word Reading (ID: 137)
- Decoding (ID: 138)
- Sounding Out (ID: 139)
- Reading Accuracy (ID: 140)
- Self-Correction (ID: 165)
- Error Detection (ID: 166)
- Accuracy Check (ID: 170)
- Progress Monitoring (ID: 171)
- Formative Assessment (ID: 172)
Orphaned Nodes Analysis¶
- Total Orphaned Nodes: 64
Concepts that are not prerequisites for any other concept:
- 12: Sentence
- 78: Syllable Clapping
- 80: Onset and Rime
- 83: Sound of B
- 84: Sound of C
- 85: Sound of D
- 86: Sound of F
- 87: Sound of G
- 88: Sound of H
- 89: Sound of J
- 90: Sound of K
- 91: Sound of L
- 92: Sound of M
- 93: Sound of N
- 94: Sound of P
- 95: Sound of Q
- 96: Sound of R
- 97: Sound of S
- 98: Sound of T
- 99: Sound of V
...and 44 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 | 15 | Letter Name | 26 |
| 2 | 82 | Consonant Sound | 24 |
| 3 | 142 | High-Frequency Word | 18 |
| 4 | 106 | Short Vowel Sound | 8 |
| 5 | 5 | Words | 7 |
| 6 | 112 | Long Vowel Sound | 5 |
| 7 | 14 | Letter | 4 |
| 8 | 68 | Phonemic Awareness | 4 |
| 9 | 1 | Spoken Language | 3 |
| 10 | 6 | Phoneme | 3 |
Outdegree Distribution¶
| Dependencies | Number of Concepts |
|---|---|
| 0 | 2 |
| 1 | 126 |
| 2 | 63 |
| 3 | 4 |
Recommendations¶
- ⚠️ Many orphaned nodes (64): Consider if these should be prerequisites for advanced concepts
- ℹ️ Long dependency chains (26): Ensure students can follow extended learning paths
- ℹ️ Consider adding cross-dependencies: More connections could create richer learning pathways
Report generated by learning-graph-reports/analyze_graph.py