Where Digraphs Appear

Graph Theory · Axiom Academy

Discover how directed graphs model one-way relationships in the real world, from web links to food chains. On social media, you can follow someone without them following you back. Click on users to see who they follow! Web pages link to other pages, but those pages might not link back. Explore how PageRank works by clicking pages! Step 3: Dependencies & Prerequisites Some tasks must be completed before others. Click to explore different dependency scenarios! Step 4: State Machines & Workflows Systems transition from one state to another following specific rules. Watch a simple workflow in action! In nature, energy flows in one direction: from prey to predator. Click on species to see who eats whom! A directed graph (digraph) has edges with arrows showing direction. This models asymmetric relationships where the connection from A to B is different from B to A - or might not exist at all! Social media follows (you follow celebrities who don't follow back), web links (PageRank's foundation), dependencies (prerequisites, build order), state transitions (workflows, protocols), and ecological flows (food chains, energy transfer). Directed graphs require specialized algorithms: topological sorting (finding valid orderings), strongly connected components (finding mutual reachability), PageRank (measuring importance), and cycle detection (finding circular dependencies).

This is the written version of the interactive lesson above. See the full Graph Theory course.