Learning Graph Quality Metrics Report
Overview
- Total Concepts: 500
- Foundational Concepts (no dependencies): 3
- Concepts with Dependencies: 497
- Average Dependencies per Concept: 1.76
Graph Structure Validation
- Valid DAG Structure: ✅ Yes
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts
These concepts have no prerequisites:
- 1: Matter
- 2: Energy
- 11: Scientific Method
Dependency Chain Analysis
- Maximum Dependency Chain Length: 33
Longest Learning Path:
- Matter (ID: 1)
- Atoms (ID: 3)
- Atomic Theory History (ID: 25)
- Subatomic Particles (ID: 26)
- Electrons (ID: 29)
- Bohr Model (ID: 46)
- Quantum Mechanical Model (ID: 47)
- Energy Levels (ID: 48)
- Principal Quantum Number (ID: 49)
- Subshells (ID: 50)
- Orbitals (ID: 51)
- Electron Configuration (ID: 53)
- Valence Electrons (ID: 57)
- Chemical Bonds (ID: 81)
- Covalent Bonds (ID: 83)
- Lewis Structures (ID: 96)
- Lone Pairs (ID: 101)
- VSEPR Theory (ID: 113)
- Electron Geometry (ID: 114)
- Molecular Geometry (ID: 115)
- Dipole Moment (ID: 135)
- Molecular Polarity (ID: 136)
- Polar Molecules (ID: 137)
- Intermolecular Forces (ID: 141)
- States of Matter (ID: 151)
- Kinetic Molecular Theory (ID: 152)
- Gases (ID: 160)
- Ideal Gas Law (ID: 163)
- Dalton's Law (ID: 168)
- Partial Pressures (ID: 169)
- Mole Fraction (ID: 170)
- Colligative Properties (ID: 198)
- Boiling Point Elevation (ID: 199)
Orphaned Nodes Analysis
- Total Orphaned Nodes: 200
Concepts that are not prerequisites for any other concept:
- 9: Physical Changes
- 16: Density
- 20: Percent Error
- 21: Laboratory Safety
- 36: Mass Spectrum Analysis
- 37: Relative Abundance
- 45: Combustion Analysis
- 52: Orbital Shapes
- 54: Aufbau Principle
- 55: Pauli Exclusion Principle
- 56: Hund's Rule
- 58: Core Electrons
- 59: Noble Gas Notation
- 60: Electron Config of Ions
- 66: Photoelectric Effect
- 70: PES Data Interpretation
- 75: Ionic Radius
- 77: Successive Ionization Energy
- 80: Effective Nuclear Charge
- 84: Metallic Bonds
...and 180 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 | 2 | Energy | 17 |
| 2 | 115 | Molecular Geometry | 11 |
| 3 | 141 | Intermolecular Forces | 11 |
| 4 | 163 | Ideal Gas Law | 11 |
| 5 | 266 | Reaction Rate | 11 |
| 6 | 376 | Chemical Equilibrium | 11 |
| 7 | 23 | Graphing Data | 10 |
| 8 | 321 | Thermodynamics | 10 |
| 9 | 38 | Mole Concept | 9 |
| 10 | 53 | Electron Configuration | 9 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 3 |
| 1 | 165 |
| 2 | 288 |
| 3 | 42 |
| 4 | 2 |
Recommendations
- ⚠️ Many orphaned nodes (200): Consider if these should be prerequisites for advanced concepts
- ℹ️ Long dependency chains (33): Ensure students can follow extended learning paths
Report generated by learning-graph-reports/analyze_graph.py