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Learning Graph Quality Metrics Report

Overview

  • Total Concepts: 500
  • Foundational Concepts (no prerequisites, other concepts depend on them): 7
  • Terminal Nodes (nothing depends on them, but have prerequisites): 221
  • Orphaned Nodes (completely disconnected, no edges): 0
  • Concepts with Dependencies: 493
  • Average Dependencies per Concept: 1.97

Graph Structure Validation

  • Valid DAG Structure: ✅ Yes
  • Self-Dependencies: None detected ✅
  • Cycles Detected: 0

Foundational Concepts

These concepts have no prerequisites:

  • 1: Electric Current
  • 2: Voltage
  • 3: Resistance
  • 7: Circuit
  • 13: Ground
  • 17: Component Lead
  • 24: Electric Charge

Dependency Chain Analysis

  • Maximum Dependency Chain Length: 19

Longest Learning Path:

  1. Resistance (ID: 3)
  2. Conductivity (ID: 38)
  3. Conductor (ID: 71)
  4. Semiconductor Material (ID: 72)
  5. Transistor (ID: 171)
  6. Transistor Base (ID: 174)
  7. Transistor Switching (ID: 177)
  8. Logical NOT Operation (ID: 455)
  9. Logic Gate Symbol (ID: 460)
  10. OR Gate (ID: 463)
  11. NOR Gate (ID: 470)
  12. RS Latch (ID: 475)
  13. Set Input (ID: 476)
  14. Reset Input (ID: 477)
  15. Latch State (ID: 478)
  16. Memory Cell (ID: 481)
  17. Bistable Circuit (ID: 482)
  18. Oscillator Circuit (ID: 484)
  19. LED Flasher (ID: 485)

Terminal Nodes Analysis

Terminal nodes are concepts that nothing else depends on but have prerequisites. They represent natural endpoints of learning paths — culminating or specialized concepts.

  • Total Terminal Nodes: 221 (44.2% of all concepts)
  • Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

  • 23: Conventional Current
  • 31: Kirchhoff's Current Law
  • 32: Kirchhoff's Voltage Law
  • 40: Volt
  • 43: Milliampere
  • 44: Microampere
  • 45: Kilohm
  • 46: Megohm
  • 47: Coulomb
  • 48: Milliwatt
  • 50: Fuse Protection
  • 53: Battery Safety
  • 54: Short Circuit Risk
  • 56: Loop Current
  • 59: Equivalent Resistance
  • 60: Voltage Reference
  • 61: Series-Parallel Circuit
  • 62: Current Divider
  • 63: Circuit Topology
  • 64: Circuit Branch

...and 201 more

Orphaned Nodes Analysis

Orphaned nodes are completely disconnected concepts with no inbound AND no outbound edges. These indicate a quality problem — every concept should connect to the graph.

  • Total Orphaned Nodes: 0

✅ No orphaned nodes detected. All concepts are connected to the graph.

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 2 Voltage 29
2 1 Electric Current 28
3 3 Resistance 23
4 96 Resistor 20
5 110 Capacitor 20
6 120 Diode 19
7 7 Circuit 17
8 234 Push Button 16
9 171 Transistor 14
10 274 Light Emitting Diode 14

Outdegree Distribution

Dependencies Number of Concepts
0 7
1 98
2 314
3 77
4 4

Recommendations

  • ℹ️ High terminal node percentage (44.2%): Consider if some terminal concepts should be prerequisites for advanced concepts
  • ✅ DAG structure verified: Graph supports valid learning progressions
  • ℹ️ Long dependency chains (19): Ensure students can follow extended learning paths

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