How to prove max number of connection between n nodes is n*(n-1)/2
Given n nodes, if every node is connected to every other node (except itself) the number of connections will be n*(n-1)/2
How does one prove this ?
This is not a homework question. I have been away from CS text books for long and have forgotten the theory on how to prove this.
Solution
And one more solution, combinatorial: The problem is equivalent to the number of possible pairs of nodes in the graph, i.e.:
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