K-edge-connected graph

Okay, so imagine you have a bunch of dots on paper. These dots are called vertices. They are like little islands. Now, you can draw lines between some of these dots to connect them. These lines are called edges.

A k-edge-connected graph is when you have a bunch of dots (vertices) that are connected by lines (edges) in such a way that even if you erase k edges, the dots will still be connected to each other.

Let's say you have a graph with 5 dots and 6 edges. If you erase any 3 edges from this graph, the dots will still be connected to each other. This graph is called 3-edge-connected.

It's like building a bridge between two islands. If the bridge has 3 separate ropes holding it up and you cut one of them, the bridge will still stand because the other two ropes are still holding it up.

So in a k-edge-connected graph, the dots are connected by enough edges that even if some of the edges are gone, the dots will still be able to communicate with each other (like people on different islands talking to each other using walkie-talkies).