Learning Graph Quality Metrics Report

Overview

• Total Concepts: 390
• Foundational Concepts (no prerequisites, other concepts depend on them): 1
• Terminal Nodes (nothing depends on them, but have prerequisites): 222
• Orphaned Nodes (completely disconnected, no edges): 0
• Concepts with Dependencies: 389
• Average Dependencies per Concept: 1.22

Graph Structure Validation

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

Foundational Concepts

These concepts have no prerequisites:

• 1: Cybersecurity

Dependency Chain Analysis

• Maximum Dependency Chain Length: 13

Longest Learning Path:

1. Cybersecurity (ID: 1)
2. Information Security (ID: 2)
3. Confidentiality (ID: 3)
4. Cryptography (ID: 57)
5. Plaintext (ID: 58)
6. Encryption (ID: 60)
7. Cryptographic Key (ID: 62)
8. Asymmetric Cryptography (ID: 76)
9. Digital Signature (ID: 91)
10. Certificate Authority (ID: 92)
11. X.509 Certificate (ID: 94)
12. Certificate Revocation (ID: 96)
13. OCSP (ID: 97)

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: 222 (56.9% of all concepts)
• Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

• 10: Non-Repudiation
• 11: AAA Framework
• 15: STRIDE
• 16: PASTA
• 17: Attack Trees
• 24: Separation of Duties
• 25: Fail Secure Default
• 26: Complete Mediation
• 27: Open Design Principle
• 28: Economy of Mechanism
• 30: Security Economics
• 36: Blast Radius
• 37: Trust Boundary
• 39: Security Requirement
• 41: CVSS
• 43: Indicator of Compromise
• 44: Indicator of Attack
• 45: Zero Day
• 47: Cyber Kill Chain
• 48: Diamond Model

...and 202 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	1	Cybersecurity	26
2	175	Network Security	21
3	121	OWASP Top Ten	13
4	7	Authentication	11
5	318	Cyber Law	11
6	76	Asymmetric Cryptography	10
7	3	Confidentiality	9
8	21	Risk Assessment	9
9	32	Vulnerability	9
10	83	Hash Function	9

Outdegree Distribution

Dependencies	Number of Concepts
0	1
1	308
2	75
3	6

Recommendations

• ℹ️ High terminal node percentage (56.9%): Consider if some terminal concepts should be prerequisites for advanced concepts
• ✅ DAG structure verified: Graph supports valid learning progressions
• ℹ️ Consider adding cross-dependencies: More connections could create richer learning pathways

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