Learning Graph Quality Metrics Report¶
Overview¶
- Total Concepts: 206
- Foundational Concepts (no dependencies): 2
- Concepts with Dependencies: 204
- Average Dependencies per Concept: 1.87
Graph Structure Validation¶
- Valid DAG Structure: ❌ No
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts¶
These concepts have no prerequisites:
- 1: Economics
- 201: Working in Teams
Dependency Chain Analysis¶
- Maximum Dependency Chain Length: 20
Longest Learning Path:¶
- Economics (ID: 1)
- Scarcity (ID: 2)
- Opportunity Cost (ID: 3)
- Trade-offs (ID: 4)
- Marginal Analysis (ID: 5)
- Rational Decision Making (ID: 7)
- Economic Models (ID: 8)
- Microeconomics (ID: 11)
- Demand (ID: 19)
- Law of Demand (ID: 20)
- Demand Curve (ID: 21)
- Market Equilibrium (ID: 33)
- Equilibrium Price (ID: 34)
- Consumer Surplus (ID: 44)
- Deadweight Loss (ID: 80)
- Government Intervention (ID: 81)
- Fiscal Policy (ID: 126)
- Government Spending (ID: 127)
- Budget Deficit (ID: 129)
- National Debt (ID: 130)
Orphaned Nodes Analysis¶
- Total Orphaned Nodes: 65
Concepts that are not prerequisites for any other concept:
- 15: Mixed Economy
- 25: Inferior Goods
- 27: Complementary Goods
- 32: Determinants of Supply
- 37: Price Mechanism
- 38: Price Ceiling
- 39: Price Floor
- 43: Inelastic Demand
- 50: Budget Constraint
- 53: Diminishing Returns
- 60: Profit Maximization
- 63: Price Taker
- 65: Natural Monopoly
- 69: Product Differentiation
- 75: Positive Externality
- 77: Free Rider Problem
- 79: Tragedy of the Commons
- 83: Subsidies
- 84: Pigouvian Tax
- 86: Antitrust Policy
...and 45 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 | 1 | Economics | 19 |
| 2 | 3 | Opportunity Cost | 11 |
| 3 | 19 | Demand | 10 |
| 4 | 8 | Economic Models | 9 |
| 5 | 12 | Macroeconomics | 8 |
| 6 | 5 | Marginal Analysis | 7 |
| 7 | 28 | Supply | 7 |
| 8 | 34 | Equilibrium Price | 7 |
| 9 | 143 | International Trade | 7 |
| 10 | 183 | Digital Economy | 7 |
Outdegree Distribution¶
| Dependencies | Number of Concepts |
|---|---|
| 0 | 2 |
| 1 | 58 |
| 2 | 118 |
| 3 | 25 |
| 4 | 3 |
Recommendations¶
- ⚠️ Many orphaned nodes (65): Consider if these should be prerequisites for advanced concepts
- ℹ️ Long dependency chains (20): Ensure students can follow extended learning paths
Report generated by learning-graph-reports/analyze_graph.py