Learning Graph Quality Metrics Report
Overview
- Total Concepts: 380
- Foundational Concepts (no dependencies): 6
- Concepts with Dependencies: 374
- Average Dependencies per Concept: 2.07
Graph Structure Validation
- Valid DAG Structure: ❌ No
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts
These concepts have no prerequisites:
- 1: Scientific Method
- 5: Atomic Structure
- 49: Cell Theory
- 92: Thermodynamics
- 271: History of Evolutionary Thought
- 320: Ecology Overview
Dependency Chain Analysis
- Maximum Dependency Chain Length: 25
Longest Learning Path:
- Cell Theory (ID: 49)
- Eukaryotic Cells (ID: 51)
- Cytoskeleton (ID: 83)
- Microtubules (ID: 85)
- Cell Cycle Overview (ID: 161)
- Mitosis (ID: 165)
- Meiosis Overview (ID: 177)
- Meiosis I (ID: 178)
- Synapsis and Tetrad Formation (ID: 180)
- Crossing Over (ID: 181)
- Chiasmata (ID: 182)
- Genetic Recombination (ID: 183)
- Variation in Populations (ID: 274)
- Heritability (ID: 275)
- Natural Selection (ID: 273)
- Population Genetics (ID: 287)
- Allele Frequency (ID: 288)
- Hardy-Weinberg Equilibrium (ID: 289)
- Speciation Overview (ID: 300)
- Reproductive Isolation (ID: 302)
- Prezygotic Barriers (ID: 303)
- Allopatric Speciation (ID: 305)
- Adaptive Radiation (ID: 307)
- Macroevolution (ID: 315)
- Mass Extinctions (ID: 316)
Orphaned Nodes Analysis
- Total Orphaned Nodes: 119
Concepts that are not prerequisites for any other concept:
- 8: Ionic Bonds
- 11: Van der Waals Forces
- 14: Surface Tension
- 15: Specific Heat Capacity
- 20: Buffers
- 29: Polysaccharides
- 30: Glycosidic Bonds
- 33: Saturated and Unsaturated Fats
- 34: Triglycerides
- 44: Protein Denaturation
- 52: Cell Size and Surface Area Ratio
- 57: Cholesterol in Membranes
- 63: Turgor Pressure
- 66: Sodium-Potassium Pump
- 68: Exocytosis
- 69: Phagocytosis
- 70: Pinocytosis
- 72: Nuclear Envelope
- 76: Smooth ER
- 78: Lysosomes
...and 99 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 | 51 | Eukaryotic Cells | 23 |
| 2 | 103 | Enzymes | 16 |
| 3 | 22 | Functional Groups | 12 |
| 4 | 273 | Natural Selection | 12 |
| 5 | 37 | Proteins | 11 |
| 6 | 53 | Plasma Membrane | 11 |
| 7 | 193 | Monohybrid Crosses | 11 |
| 8 | 218 | DNA Replication | 10 |
| 9 | 1 | Scientific Method | 9 |
| 10 | 12 | Water Polarity | 9 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 6 |
| 1 | 104 |
| 2 | 161 |
| 3 | 89 |
| 4 | 19 |
| 5 | 1 |
Recommendations
- ⚠️ Many orphaned nodes (119): Consider if these should be prerequisites for advanced concepts
- ℹ️ Long dependency chains (25): Ensure students can follow extended learning paths
Report generated by learning-graph-reports/analyze_graph.py