Learning Graph Quality Metrics Report

Overview

• Total Concepts: 338
• Foundational Concepts (no prerequisites, other concepts depend on them): 4
• Terminal Nodes (nothing depends on them, but have prerequisites): 155
• Orphaned Nodes (completely disconnected, no edges): 0
• Concepts with Dependencies: 334
• Average Dependencies per Concept: 1.57

Graph Structure Validation

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

Foundational Concepts

These concepts have no prerequisites:

• 1: Computer Network
• 15: Standard
• 21: Bit
• 71: Signal

Dependency Chain Analysis

• Maximum Dependency Chain Length: 16

Longest Learning Path:

1. Bit (ID: 21)
2. Byte (ID: 22)
3. Header (ID: 28)
4. Encapsulation (ID: 31)
5. Layered Architecture (ID: 33)
6. OSI Reference Model (ID: 34)
7. Network Layer (ID: 38)
8. Routing (ID: 171)
9. Routing Algorithm (ID: 176)
10. Path Vector Routing (ID: 186)
11. BGP Protocol (ID: 187)
12. Autonomous System (ID: 188)
13. Internet Topology (ID: 191)
14. Content Delivery Network (ID: 324)
15. Edge Computing (ID: 325)
16. Fog Computing (ID: 326)

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: 155 (45.9% of all concepts)
• Healthy Range: 5-40% of total concepts

Concepts at the end of learning paths:

• 7: Network Edge
• 18: IETF
• 19: ISO
• 20: ICANN
• 27: Message
• 30: Trailer
• 32: Decapsulation
• 40: Session Layer
• 41: Presentation Layer
• 43: End To End Principle
• 44: Separation Of Concerns
• 48: Best Effort Delivery
• 51: Stateless Protocol
• 52: In Band Signaling
• 53: Out Of Band Signaling
• 54: Unicast
• 60: Goodput
• 62: Propagation Delay
• 63: Transmission Delay
• 65: Processing Delay

...and 135 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	16	RFC Document	18
2	199	TCP	17
3	42	Application Layer	16
4	38	Network Layer	14
5	12	IP Address	11
6	14	Protocol	11
7	22	Byte	9
8	1	Computer Network	8
9	61	Latency	8
10	239	HTTP Protocol	8

Outdegree Distribution

Dependencies	Number of Concepts
0	4
1	174
2	141
3	11
4	6
5	2

Recommendations

• ℹ️ High terminal node percentage (45.9%): Consider if some terminal concepts should be prerequisites for advanced concepts
• ✅ DAG structure verified: Graph supports valid learning progressions
• ℹ️ Long dependency chains (16): Ensure students can follow extended learning paths

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