Learning Graph Quality Metrics Report
Overview
- Total Concepts: 410
- Foundational Concepts (no dependencies): 2
- Concepts with Dependencies: 408
- Average Dependencies per Concept: 2.13
Graph Structure Validation
- Valid DAG Structure: ✅ Yes
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts
These concepts have no prerequisites:
- 1: Digital Systems
- 4: Decimal Number System
Dependency Chain Analysis
- Maximum Dependency Chain Length: 38
Longest Learning Path:
- Digital Systems (ID: 1)
- Binary Number System (ID: 3)
- Boolean Algebra (ID: 41)
- Boolean Variable (ID: 42)
- Truth Value (ID: 46)
- AND Operation (ID: 47)
- Boolean Expression (ID: 65)
- Literal (ID: 81)
- Product Term (ID: 82)
- Minterm (ID: 128)
- Karnaugh Map (ID: 161)
- K-Map Structure (ID: 162)
- K-Map Gray Code Order (ID: 169)
- K-Map Adjacency (ID: 170)
- Logical Adjacency (ID: 171)
- K-Map Grouping (ID: 173)
- Implicant (ID: 180)
- Prime Implicant (ID: 181)
- Essential Prime Implicant (ID: 182)
- K-Map SOP Simplification (ID: 184)
- Minimal SOP Expression (ID: 186)
- Quine-McCluskey Algorithm (ID: 201)
- Tabular Minimization Method (ID: 202)
- Implicant Table Construction (ID: 203)
- Grouping by Number of Ones (ID: 205)
- Adjacency Criterion in QM (ID: 206)
- Combining Adjacent Minterms (ID: 207)
- Dash Notation for Combined Terms (ID: 208)
- Iterative Combination Process (ID: 209)
- Unchecked Terms as Prime Implicants (ID: 210)
- Prime Implicant Chart Construction (ID: 211)
- Essential Prime Implicants Selection (ID: 212)
- Row Dominance (ID: 213)
- Cyclic Prime Implicant Charts (ID: 215)
- Petrick's Method (ID: 216)
- Minimal Cover Selection (ID: 217)
- Multi-Output Function Minimization (ID: 221)
- Systematic Approach Advantages (ID: 225)
Orphaned Nodes Analysis
- Total Orphaned Nodes: 116
Concepts that are not prerequisites for any other concept:
- 2: Analog vs Digital Signals
- 9: Radix Point
- 13: Word
- 16: Binary to Decimal Conversion
- 17: Decimal to Binary Conversion
- 18: Octal to Decimal Conversion
- 19: Decimal to Octal Conversion
- 20: Hexadecimal to Decimal
- 21: Decimal to Hexadecimal
- 22: Binary to Octal Conversion
- 23: Octal to Binary Conversion
- 24: Binary to Hexadecimal
- 25: Hexadecimal to Binary
- 29: Binary Division
- 31: Unsigned Numbers
- 35: Sign Extension
- 39: Underflow
- 40: Range of Signed Numbers
- 59: XNOR Gate
- 63: IEEE Gate Symbols
...and 96 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 | 3 | Binary Number System | 20 |
| 2 | 41 | Boolean Algebra | 15 |
| 3 | 47 | AND Operation | 14 |
| 4 | 48 | OR Operation | 14 |
| 5 | 51 | Logic Gates | 14 |
| 6 | 64 | Truth Table | 13 |
| 7 | 93 | Logic Circuit | 12 |
| 8 | 128 | Minterm | 12 |
| 9 | 4 | Decimal Number System | 11 |
| 10 | 91 | Combinational Logic | 11 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 2 |
| 1 | 69 |
| 2 | 237 |
| 3 | 88 |
| 4 | 13 |
| 10 | 1 |
Recommendations
- ⚠️ Many orphaned nodes (116): Consider if these should be prerequisites for advanced concepts
- ✅ DAG structure verified: Graph supports valid learning progressions
- ℹ️ Long dependency chains (38): Ensure students can follow extended learning paths
Report generated by learning-graph-reports/analyze_graph.py