Learning Graph Quality Metrics Report
Overview
- Total Concepts: 400
- Foundational Concepts (no dependencies): 1
- Concepts with Dependencies: 399
- Average Dependencies per Concept: 1.54
Graph Structure Validation
- Valid DAG Structure: ❌ No
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts
These concepts have no prerequisites:
- 1: Computer Science
Dependency Chain Analysis
- Maximum Dependency Chain Length: 16
Longest Learning Path:
- Computer Science (ID: 1)
- Programming Languages (ID: 17)
- Compiled vs Interpreted (ID: 18)
- Python Language (ID: 19)
- Data Types (ID: 27)
- Integer Type (ID: 28)
- Arithmetic Operators (ID: 36)
- Expressions (ID: 48)
- Statements (ID: 49)
- Control Flow (ID: 66)
- Loops (ID: 75)
- For Loop (ID: 76)
- List Traversal (ID: 166)
- Linear Search (ID: 329)
- Binary Search (ID: 330)
- Search Comparison (ID: 331)
Orphaned Nodes Analysis
- Total Orphaned Nodes: 204
Concepts that are not prerequisites for any other concept:
- 12: ASCII and Unicode
- 16: Operating Systems
- 21: Python REPL
- 32: Type Function
- 34: Implicit Type Conversion
- 37: Integer Division
- 38: Modulo Operator
- 42: F-String Formatting
- 46: Constants Convention
- 54: Greater and Less Than
- 59: Short-Circuit Evaluation
- 61: Boolean Conversion
- 62: Chained Comparisons
- 63: Order of Operations
- 64: De Morgan's Laws
- 65: Truth Tables
- 67: Sequential Execution
- 72: Nested Conditionals
- 73: Ternary Expression
- 74: Match Statement
...and 184 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 | 151 | Lists | 29 |
| 2 | 206 | Dictionaries | 18 |
| 3 | 326 | Algorithm Design | 16 |
| 4 | 27 | Data Types | 13 |
| 5 | 76 | For Loop | 12 |
| 6 | 116 | Functions | 12 |
| 7 | 341 | Time Complexity | 12 |
| 8 | 25 | Variable Assignment | 10 |
| 9 | 91 | String Basics | 10 |
| 10 | 143 | Recursion | 10 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 1 |
| 1 | 211 |
| 2 | 162 |
| 3 | 23 |
| 4 | 3 |
Recommendations
- ⚠️ Many orphaned nodes (204): Consider if these should be prerequisites for advanced concepts
- ℹ️ Long dependency chains (16): Ensure students can follow extended learning paths
Report generated by learning-graph-reports/analyze_graph.py