Cycle (graph theory)

A cycle in graph theory is when we draw a picture of a bunch of dots (also called vertices) and lines (also called edges) connecting them. A cycle is when we can draw a line that starts and ends at the same dot while passing through other dots and lines on the way. It's like a circle that we draw on the paper but it can be made up of different shapes and sizes of dots and lines. For example, if we draw three dots and connect them in a triangle shape, that's a cycle because we can trace our finger around the edges of the triangle and end up back where we started. A cycle can also be made up of more dots connected in a complicated way, but as long as we can make a full loop without going over the same line twice or skipping any dots, it's still a cycle. Graph theory is like a puzzle where we try to figure out how to draw these cycles and find patterns in them.