Learning Graph for Beginning Electronics
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Overview
This learning graph represents a comprehensive knowledge structure for the Beginning Electronics course, mapping 500 interconnected concepts with their dependencies and categorical organization. It was regenerated in 2026 against a revised course description (5th-12th grade, $50 solderless-breadboard kit, no microcontrollers/programming) and then expanded from 200 to 500 concepts for maximum depth.
Purpose
The learning graph serves as foundational infrastructure for an intelligent textbook that supports:
- Personalized Learning Pathways: Students can navigate concepts based on their current knowledge
- Prerequisite Tracking: Clear visualization of concept dependencies
- Progress Monitoring: Track mastery of concepts across the curriculum
- Adaptive Content: Customize learning experiences based on student needs
Graph Statistics
- Total Concepts: 500
- Total Dependencies (edges): 973
- Average Dependencies per Concept: 1.95
- Root Concepts: 7 (foundation concepts with no prerequisites)
- Maximum Dependency Chain Length: 19 concepts deep (18 levels)
- Taxonomy Categories: 10
- Orphaned Nodes: 0
- Connected Components: 1 (fully connected)
Files
Core Data Files
- learning-graph.csv -
ConceptID,ConceptLabel,Dependencies,TaxonomyID(pipe-delimited dependency IDs) - learning-graph.json - vis.js network format for visualization, includes metadata, groups, nodes, and edges
- taxonomy-names.json - Maps each TaxonomyID to its human-readable category name
- color-config.json - Maps each TaxonomyID to a distinct display color
- metadata.json - Title, description, creator, version, and license for the graph
Analysis and Reports
- step-01-course-assessment.md - Course description quality analysis (score: 98/100)
- step-02-concepts.md - Complete list of 500 concepts with categorization
- step-04-quality-analysis.md - Graph validation report (cycles, orphans, connectivity)
- step-05-taxonomy.md - Taxonomy structure and category definitions
- step-07-distribution-report.md - Taxonomy balance analysis
Python Scripts
- csv-to-json.py (v0.04) - Convert CSV to vis.js JSON format
- analyze-graph.py - Validate graph quality (DAG, connectivity, cycles)
- add-taxonomy.py - Add taxonomy IDs to concept CSV
- taxonomy-distribution.py - Generate category distribution report
- validate-learning-graph.py / validate-learning-graph.sh - Validate
learning-graph.jsonagainst the schema
Taxonomy Categories
| TaxonomyID | Category | Count | Percentage | Description |
|---|---|---|---|---|
| FOUND | Foundational Concepts | 95 | 19.0% | Core electrical theory, units, and safety |
| PASV | Passive Components | 75 | 15.0% | Resistors, capacitors, diodes, LEDs |
| ACTV | Active Components & ICs | 63 | 12.6% | Transistors, 555 timer, 74HC595 shift register |
| BRDG | Breadboarding & Assembly | 58 | 11.6% | Wiring skills, troubleshooting, optional perfboard packaging |
| INPT | Input Components | 40 | 8.0% | Switches, buttons, wired logic, light sensing |
| OUTP | Output Components | 40 | 8.0% | LEDs, RGB mixing, motors, buzzers |
| PWR | Power Systems | 40 | 8.0% | Batteries, regulators, buck converters, solar |
| MEAS | Measurement & Testing | 38 | 7.6% | Multimeter use, systematic troubleshooting |
| DLOG | Digital Logic & Boolean | 30 | 6.0% | Transistor-built logic gates, RS latch |
| CAPS | Advanced Circuits & Capstone Projects | 21 | 4.2% | Timing/memory circuits, named real-world projects, capstone planning |
Foundation Concepts (Root Nodes)
These 7 concepts have no prerequisites and form the foundation of the curriculum:
- Electric Current - Fundamental electrical phenomenon
- Voltage - Electrical potential difference
- Resistance - Opposition to current flow
- Circuit - A closed path for current to flow
- Ground - The reference point for a circuit
- Component Lead - Physical structure of components
- Electric Charge - The underlying property that creates current and voltage
Most Central Concepts (High In-Degree)
These concepts are depended upon by many other concepts:
- Voltage - 29 dependents
- Electric Current - 28 dependents
- Resistance - 23 dependents
- Resistor - 20 dependents
- Capacitor - 20 dependents
- Diode - 19 dependents
- Circuit - 17 dependents
- Push Button - 16 dependents
- Transistor - 14 dependents
- Light Emitting Diode - 14 dependents
Graph Quality
✓ Valid DAG: No cycles detected, no self-dependencies
✓ Fully Connected: Single connected component
✓ No Orphans: All 500 concepts integrated into the graph
✓ Balanced Distribution: All 10 categories under the 30% threshold (range: 4.2%-19.0%)
Depth Distribution
| Level | Concept Count | Description |
|---|---|---|
| 0 | 7 | Foundation concepts (no dependencies) |
| 1 | 24 | First-level concepts |
| 2 | 55 | Second-level concepts |
| 3 | 75 | Third-level concepts |
| 4 | 54 | Fourth-level concepts |
| 5 | 61 | Fifth-level concepts |
| 6 | 49 | Sixth-level concepts |
| 7 | 61 | Seventh-level concepts |
| 8 | 39 | Eighth-level concepts |
| 9 | 29 | Ninth-level concepts |
| 10 | 21 | Tenth-level concepts |
| 11-18 | 25 | Deepest, most advanced/integrative concepts (capstone-adjacent) |
Using the Learning Graph
For Students
The learning graph helps you:
- Understand what concepts you need to master first
- See how concepts build upon each other
- Track your progress through the curriculum
- Find gaps in your knowledge
For Instructors
The learning graph enables you to:
- Design optimal learning sequences
- Identify prerequisite knowledge for each lesson
- Create customized learning paths for different students
- Assess student readiness for advanced topics
For Developers
The graph data can be used to:
- Build interactive visualization tools
- Create adaptive learning systems
- Generate personalized study plans
- Track learning analytics
Visualization
The learning-graph.json file can be visualized using vis.js or similar network visualization libraries. The JSON structure includes:
- Nodes: Each concept with ID, label, and group (TaxonomyID)
- Edges: Directed edges showing dependencies (prerequisite → dependent concept)
- Groups: Taxonomy categories with
classifierNameand displaycolor
To install an interactive graph-viewer MicroSim for this data, run the book-installer skill's "install learning graph viewer" guide.
Course Alignment
This learning graph aligns with the Beginning Electronics course structure:
- Bloom's Taxonomy: Concepts progress from Remember/Understand through Create
- Hands-On Focus: Emphasis on practical breadboarding and testing skills
- $50 Kit, No Soldering Required: Focus on accessible, affordable, solderless parts
- No Microcontrollers or Programming: Complements the companion Learning MicroPython and Physical Computing course
- Interactive Learning: Integration with MicroSims and simulations
Maintenance
To update the learning graph:
- Edit
learning-graph.csvto add/modify concepts (columns:ConceptID,ConceptLabel,Dependencies,TaxonomyID) - Run
python3 analyze-graph.py learning-graph.csv step-04-quality-analysis.mdto validate quality - Run
python3 taxonomy-distribution.py learning-graph.csv step-07-distribution-report.md taxonomy-names.jsonto check balance - Run
python3 csv-to-json.py learning-graph.csv learning-graph.json color-config.json metadata.json taxonomy-names.jsonto regenerate the JSON - Run
./validate-learning-graph.sh learning-graph.jsonto validate against the schema
References
- Course Site: Beginning Electronics
- Learning Graphs Repository: dmccreary/learning-graphs
- Visualization Library: vis.js Network
Contact
For questions about the learning graph structure or usage, see the main course contact page.
Generated using the learning-graph-generator skill (v0.05) Last updated: 2026-08-14