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Graphs have varying degrees of connection. The higher the ratio of edges to vertices, the more connected the graph.

This graph represents a social network; people are vertices and edges are friendships. Ted is adjacent to Patty, Ron, and Alice because an edge directly connects them.

We use a single line for an edge, but these friendships are bi-directional. Patty is friends with Ron and Ron is friends with Patty.

A path is vertices which are connected by any number of intermediate edges. The paths from Alice to Patty could go Alice to Ted to Patty or, Alice to Ted to Ron to Patty.

No path exists between Sally and Ted. When no path exists between two vertices, a graph is disconnected.

Instructions

What are the paths that connect Ron to Ted?

What edge could we add that would change this into a connected graph?

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