Connected vs Disconnected

Graph Theory · Axiom Academy

INTRO Connected vs Disconnected Can you get there from here? The fundamental question of graph connectivity. Imagine a group of islands. Some have bridges connecting them, others don't. Click on different islands to explore! Think about a computer network. When a cable breaks, what happens? Click on a connection to remove it! From Real World to Graph Theory Let's see how mathematicians think about this. Choose a graph type to explore: In a connected graph, you can always find a path. Click on two vertices to see a path between them! One piece. Every vertex is reachable from every other vertex. There exists a path between any pair of vertices. Example: A functional transportation network, a complete social network. Multiple pieces (components). Some vertices cannot reach others. At least one pair of vertices has no path between them. Example: Separate island groups, broken network, isolated communities. Connectivity determines if a network is functional, if a system can communicate, if a structure is stable. It's one of the most fundamental properties in graph theory.

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