Learning Graph Quality Metrics Report
Overview
- Total Concepts: 288
- Foundational Concepts (no prerequisites, other concepts depend on them): 10
- Terminal Nodes (nothing depends on them, but have prerequisites): 158
- Orphaned Nodes (completely disconnected, no edges): 0
- Concepts with Dependencies: 278
- Average Dependencies per Concept: 1.60
Graph Structure Validation
- Valid DAG Structure: ✅ Yes
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts
These concepts have no prerequisites:
- 1: Native Plant Definition
- 5: Botany Fundamentals
- 6: Ecosystem Definition
- 17: USDA Hardiness Zones
- 216: MN DNR Programs
- 230: U Of MN Extension
- 236: MN Native Plant Society
- 241: Systems Thinking Overview
- 259: Evidence-Based Practices
- 274: Critical Thinking Basics
Dependency Chain Analysis
- Maximum Dependency Chain Length: 11
Longest Learning Path:
- Ecosystem Definition (ID: 6)
- Habitat (ID: 8)
- Minnesota Ecoregions (ID: 11)
- Deciduous Forest Region (ID: 13)
- Woodland Ecosystem Overview (ID: 46)
- Forest Layers (ID: 47)
- Ground Cover Layer (ID: 50)
- Spring Ephemerals (ID: 51)
- Spring Bloom Plants (ID: 199)
- Seasonal Bloom Sequence (ID: 152)
- Bloom Timing Pollinators (ID: 103)
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: 158 (54.9% of all concepts)
- Healthy Range: 5-40% of total concepts
Concepts at the end of learning paths:
- 10: Scientific Nomenclature
- 14: Coniferous Forest Region
- 15: Prairie-Forest Border
- 19: Growing Season Length
- 23: Prairie Remnants
- 25: Big Bluestem
- 26: Little Bluestem
- 27: Switchgrass
- 28: Indian Grass
- 29: Prairie Dropseed
- 31: Purple Coneflower
- 32: Black-Eyed Susan
- 33: Wild Bergamot
- 34: Blazing Star
- 35: Prairie Clover
- 44: Warm Season Grasses
- 45: Cool Season Grasses
- 52: Bloodroot
- 53: Trillium
- 54: Hepatica
...and 138 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 | 3 | Invasive Species Definition | 14 |
| 2 | 87 | Pollinator Overview | 14 |
| 3 | 104 | Invasive Species Impact | 14 |
| 4 | 4 | Plant Identification Basics | 13 |
| 5 | 6 | Ecosystem Definition | 13 |
| 6 | 30 | Prairie Wildflowers | 13 |
| 7 | 1 | Native Plant Definition | 12 |
| 8 | 24 | Prairie Grasses | 11 |
| 9 | 150 | Native Garden Design | 11 |
| 10 | 187 | Restoration Ecology Basics | 11 |
Outdegree Distribution
| Dependencies | Number of Concepts |
|---|---|
| 0 | 10 |
| 1 | 143 |
| 2 | 116 |
| 3 | 11 |
| 4 | 4 |
| 5 | 4 |
Recommendations
- ℹ️ High terminal node percentage (54.9%): Consider if some terminal concepts should be prerequisites for advanced concepts
- ✅ DAG structure verified: Graph supports valid learning progressions
Report generated by learning-graph-reports/analyze_graph.py