How many edges are there?

Interactive challenge

Here are 6 vertices. Suppose every vertex is joined to every other vertex.

Question: How many edges will there be altogether? Try to guess first, then build the graph step by step.

Edges shown:

Keep going until every pair of vertices has been joined.

Reveal answer

There are 15 edges.

Vertex A joins to 5 others, then B adds 4 new edges, C adds 3, D adds 2, and E adds 1.

5 + 4 + 3 + 2 + 1 = 15

So a graph with 6 vertices, where every pair is joined, has 15 edges.