What happens when we relax the rules of a tree?
- In previous weeks, we studied trees. A key feature of a tree is that it is acyclic—there are no closed loops. You can't start at one node, follow a path of edges, and arrive back at your starting node without retracing your steps.
- But what if we allow cycles? What if we connect nodes in a way that creates loops?
- By removing that restriction, we get a more general structure: a Graph. A graph is simply a collection of nodes (vertices) and edges that connect them.
- This means a tree is just a special type of graph—one that is connected and has no cycles. For the next four weeks, we will explore the world of graphs, which can model a vast number of real-world systems.