Learning Graph Quality Metrics Report

Overview

• Total Concepts: 578
• Foundational Concepts (no prerequisites, other concepts depend on them): 5
• Terminal Nodes (nothing depends on them, but have prerequisites): 288
• Orphaned Nodes (completely disconnected, no edges): 0
• Concepts with Dependencies: 573
• Average Dependencies per Concept: 1.52

Graph Structure Validation

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

Foundational Concepts

These concepts have no prerequisites:

• 1: Learning Management System
• 25: RESTful API
• 428: District Administrator
• 429: Teacher
• 430: Textbook Author

Dependency Chain Analysis

• Maximum Dependency Chain Length: 21

Longest Learning Path:

1. Learning Management System (ID: 1)
2. SCORM (ID: 2)
3. Experience API (ID: 6)
4. Learning Record Store (ID: 7)
5. System Context Diagram (ID: 61)
6. Tenant (ID: 76)
7. District (ID: 77)
8. School (ID: 78)
9. Course (ID: 79)
10. Section (ID: 80)
11. Student (ID: 87)
12. Has Mastery Relationship (ID: 106)
13. Concept Mastery Vertex (ID: 114)
14. Mastery Computation Function (ID: 141)
15. Bayesian Knowledge Tracing (ID: 187)
16. Prior Mastery Probability (ID: 188)
17. Evidence Conditioning Step (ID: 192)
18. Learning Transition Step (ID: 193)
19. BKT Streaming Update (ID: 204)
20. Late Arrival Detector (ID: 206)
21. Targeted Replay Command (ID: 207)

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: 288 (49.8% of all concepts)
• Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

• 3: AICC
• 5: Sharable Content Object
• 8: Learning Record Provider
• 16: Sub-Statement
• 17: Attachment
• 18: Extensions
• 21: Registration
• 23: Inverse Functional Identifier
• 26: HTTP Verb
• 30: Basic Authentication
• 37: Determining Property
• 39: cmi5 Assignable Unit
• 40: cmi5 Launch Method
• 45: xAPI Profile Server
• 46: TLA Reference Implementation
• 47: Standards Governance
• 48: Stewardship Transition
• 49: Open Source Infrastructure
• 51: Caliper Analytics
• 52: Learning Object Metadata

...and 268 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	67	Ingestion Gateway	17
2	490	My Classes Dashboard	13
3	152	ClickHouse	12
4	252	Common Dashboard Anatomy	12
5	77	District	11
6	150	Apache Kafka	11
7	434	District Management UI	11
8	69	Event Store	10
9	70	Stream Processor	10
10	114	Concept Mastery Vertex	10

Outdegree Distribution

Dependencies	Number of Concepts
0	5
1	300
2	253
3	16
4	3
5	1

Recommendations

• ℹ️ High terminal node percentage (49.8%): Consider if some terminal concepts should be prerequisites for advanced concepts
• ✅ DAG structure verified: Graph supports valid learning progressions
• ℹ️ Long dependency chains (21): Ensure students can follow extended learning paths

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