Learning Graph Quality Metrics Report¶
Overview¶
- Total Concepts: 300
- Foundational Concepts (no prerequisites, other concepts depend on them): 7
- Terminal Nodes (nothing depends on them, but have prerequisites): 107
- Orphaned Nodes (completely disconnected, no edges): 0
- Concepts with Dependencies: 293
- Average Dependencies per Concept: 2.27
Graph Structure Validation¶
- Valid DAG Structure: ✅ Yes
- Self-Dependencies: None detected ✅
- Cycles Detected: 0
Foundational Concepts¶
These concepts have no prerequisites:
- 1: Matrix Multiplication
- 2: Matrix Transpose
- 5: Symmetric Matrix
- 11: Gradient Descent
- 13: Chain Rule (Calculus)
- 15: PyTorch Tensor
- 21: Graph (Undirected)
Dependency Chain Analysis¶
- Maximum Dependency Chain Length: 12
Longest Learning Path:¶
- Graph (Undirected) (ID: 21)
- Node (Vertex) (ID: 23)
- Edge (Link) (ID: 24)
- Heterogeneous Graph (ID: 38)
- Knowledge Graph (ID: 178)
- KG Entity (ID: 179)
- KG Triple (ID: 181)
- KG Completion (ID: 182)
- DistMult (ID: 186)
- ComplEx (ID: 187)
- RotatE (ID: 188)
- KG Embedding Geometry (ID: 189)
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: 107 (35.7% of all concepts)
- Healthy Range: 5-40% of total concepts
Concepts at the end of learning paths:
- 39: Multigraph
- 48: Planar Graph
- 54: Barabási–Albert Model
- 64: HITS Algorithm
- 68: Teleportation (PageRank)
- 71: Louvain Algorithm
- 72: Girvan-Newman Algorithm
- 74: Normalized Cut
- 76: BigCLAM Model
- 79: Graphlet Degree Vector
- 81: Weisfeiler-Lehman Kernel
- 83: Belief Propagation
- 84: Influence Maximization
- 90: Katz Similarity
- 92: Embedding Space
- 94: Shallow Embedding
- 99: BFS Strategy (node2vec)
- 100: DFS Strategy (node2vec)
- 103: LINE Embedding
- 106: Structural Equivalence
...and 87 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 | 108 | Graph Neural Network (GNN) | 72 |
| 2 | 21 | Graph (Undirected) | 34 |
| 3 | 91 | Node Embedding | 20 |
| 4 | 26 | Node Degree | 18 |
| 5 | 25 | Adjacency Matrix | 17 |
| 6 | 17 | Neural Network Layer | 16 |
| 7 | 24 | Edge (Link) | 15 |
| 8 | 23 | Node (Vertex) | 12 |
| 9 | 178 | Knowledge Graph | 11 |
| 10 | 29 | Degree Distribution | 8 |
Outdegree Distribution¶
| Dependencies | Number of Concepts |
|---|---|
| 0 | 7 |
| 1 | 46 |
| 2 | 159 |
| 3 | 64 |
| 4 | 17 |
| 5 | 5 |
| 6 | 1 |
| 10 | 1 |
Recommendations¶
- ✅ Terminal node percentage (35.7%): Within healthy range (5-40%)
- ✅ DAG structure verified: Graph supports valid learning progressions
Report generated by learning-graph-reports/analyze_graph.py