Learning Graph Quality Metrics Report

Overview

• Total Concepts: 300
• Foundational Concepts (no dependencies): 6
• Concepts with Dependencies: 294
• Average Dependencies per Concept: 1.79

Graph Structure Validation

• Valid DAG Structure: ❌ No
• Self-Dependencies: None detected ✅
• Cycles Detected: 0

Foundational Concepts

These concepts have no prerequisites:

• 1: Binary Number System
• 15: Boolean Variable
• 114: 7-Segment Display
• 148: Clock Signal
• 239: Verilog HDL
• 280: FPGA Architecture

Dependency Chain Analysis

• Maximum Dependency Chain Length: 24

Longest Learning Path:

1. Boolean Variable (ID: 15)
2. Boolean Constant (ID: 16)
3. Boolean Expression (ID: 17)
4. Boolean Function (ID: 18)
5. Truth Table (ID: 19)
6. Logic Gate (ID: 36)
7. Combinational Logic (ID: 66)
8. Memory Element (ID: 135)
9. Feedback Loop (ID: 137)
10. Bistable Element (ID: 138)
11. SR Latch (ID: 139)
12. Gated SR Latch (ID: 142)
13. D Latch (ID: 143)
14. D Flip-Flop (ID: 155)
15. Finite State Machine (ID: 180)
16. FSM State (ID: 181)
17. State Transition (ID: 182)
18. Next State (ID: 184)
19. Next State Logic (ID: 185)
20. Next State Equation (ID: 200)
21. FSM Design Process (ID: 202)
22. Sequence Detector (ID: 204)
23. Overlapping Detection (ID: 206)
24. Non-Overlapping Detection (ID: 207)

Orphaned Nodes Analysis

• Total Orphaned Nodes: 101

Concepts that are not prerequisites for any other concept:

• 2: Decimal to Binary Conversion
• 5: Hex to Binary Conversion
• 6: Octal Numbers
• 14: Weighted Codes
• 33: Dual Expression
• 34: Consensus Theorem
• 46: IEEE Gate Symbols
• 49: NAND-Only Design
• 50: NOR-Only Design
• 53: Rise Time
• 54: Fall Time
• 55: Fan-In
• 56: Fan-Out
• 59: Voltage Threshold
• 61: TTL Logic
• 62: CMOS Logic
• 64: Analog vs Digital
• 65: Signal Integrity
• 70: Multi-Level Logic
• 78: Minimal Form

...and 81 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	36	Logic Gate	19
2	66	Combinational Logic	17
3	155	D Flip-Flop	17
4	1	Binary Number System	16
5	23	Boolean Algebra	13
6	239	Verilog HDL	13
7	180	Finite State Machine	10
8	17	Boolean Expression	8
9	251	Always Block	8
10	19	Truth Table	7

Outdegree Distribution

Dependencies	Number of Concepts
0	6
1	112
2	147
3	27
4	6
5	1
10	1

Recommendations

• ⚠️ Many orphaned nodes (101): Consider if these should be prerequisites for advanced concepts
• ℹ️ Long dependency chains (24): Ensure students can follow extended learning paths

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Report generated by learning-graph-reports/analyze_graph.py