Learning Graph Quality Metrics Report
Overview
- Total Concepts: 200
- Foundational Concepts (no dependencies): 9
- Concepts with Dependencies: 191
- Average Dependencies per Concept: 1.40
Graph Structure Validation
- Valid DAG Structure: ❌ No
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts
These concepts have no prerequisites:
- 1: Money Management Principles
- 2: Financial Goal Setting
- 4: Economic Literacy
- 11: Assets and Liabilities
- 18: Commercial Banks
- 19: Credit Unions
- 54: Credit Score
- 128: Insurance Principles
- 166: Identity Theft
Dependency Chain Analysis
- Maximum Dependency Chain Length: 10
Longest Learning Path:
- Assets and Liabilities (ID: 11)
- Income Statement (ID: 13)
- Gross Income (ID: 109)
- Federal Income Tax (ID: 114)
- Tax Filing (ID: 117)
- Tax Credits (ID: 121)
- Tax Planning (ID: 126)
- Tax-Advantaged Accounts (ID: 127)
- 401(k) Plan (ID: 194)
- Employer Matching (ID: 197)
Orphaned Nodes Analysis
- Total Orphaned Nodes: 113
Concepts that are not prerequisites for any other concept:
- 7: Trade-offs
- 10: Net Worth Tracking
- 12: Personal Balance Sheet
- 16: Wealth Building Strategies
- 17: Financial Planning Process
- 23: High-Yield Savings Accounts
- 24: Account Fees
- 27: ATM Usage
- 28: Debit Cards
- 31: ACH Transfers
- 32: Wire Transfers
- 33: Peer-to-Peer Payment Apps
- 35: FDIC Insurance
- 37: 50/30/20 Rule
- 38: Zero-Based Budgeting
- 39: Envelope Method
- 40: Income Tracking
- 42: Fixed Expenses
- 43: Variable Expenses
- 44: Needs vs Wants Analysis
...and 93 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 | 128 | Insurance Principles | 13 |
| 2 | 36 | Personal Budgeting | 10 |
| 3 | 70 | Consumer Debt | 10 |
| 4 | 109 | Gross Income | 9 |
| 5 | 2 | Financial Goal Setting | 8 |
| 6 | 21 | Checking Accounts | 7 |
| 7 | 84 | Stock Market | 7 |
| 8 | 11 | Assets and Liabilities | 6 |
| 9 | 22 | Savings Accounts | 6 |
| 10 | 65 | Credit Cards | 6 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 9 |
| 1 | 121 |
| 2 | 64 |
| 3 | 6 |
Recommendations
- ⚠️ Many orphaned nodes (113): Consider if these should be prerequisites for advanced concepts
- ℹ️ Consider adding cross-dependencies: More connections could create richer learning pathways
Report generated by learning-graph-reports/analyze_graph.py