DAG Topological Ordering and Transitive Reduction

flowchart TD subgraph Full ["Full Graph - All Edges Shown"] direction TD WM1[1. Working Memory]:::blue CH1[2. Chunking]:::blue SC1[3. Schema]:::blue RP1[4. Retrieval Practice]:::blue SE1[5. Spacing Effect]:::blue DD1[6. Desirable Difficulty]:::blue DP1[7. Deliberate Practice]:::blue TR1[8. Transfer]:::blue CH1 --> WM1 SC1 --> CH1 RP1 --> WM1 SE1 --> RP1 DD1 --> SE1 DD1 --> RP1 DP1 --> DD1 DP1 --> SC1 TR1 --> SC1 TR1 --> DP1 end subgraph Reduced ["Transitive Reduction - Redundant Edge Dashed"] direction TD WM2[1. Working Memory]:::teal CH2[2. Chunking]:::teal SC2[3. Schema]:::teal RP2[4. Retrieval Practice]:::teal SE2[5. Spacing Effect]:::teal DD2[6. Desirable Difficulty]:::teal DP2[7. Deliberate Practice]:::teal TR2[8. Transfer]:::teal CH2 --> WM2 SC2 --> CH2 RP2 --> WM2 SE2 --> RP2 DD2 --> SE2 DD2 -.->|redundant| RP2 DP2 --> DD2 DP2 --> SC2 TR2 --> SC2 TR2 --> DP2 end classDef blue fill:#4A90D9,stroke:#2C5F8A,color:#fff classDef teal fill:#26A69A,stroke:#00796B,color:#fff

Left: the full graph with all ten edges. Right: the transitive reduction. The dashed edge from Desirable Difficulty to Retrieval Practice is redundant because the path through Spacing Effect already implies it. Numbers show one valid topological ordering of several possible.

A Small Learning Graph - Topological Ordering and Transitive Reduction