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The maximum number of edges in a n-node undirected graph without self loops is

1. $n^2$
2. $\frac{n(n-1)}{2}$
3. $n-1$
4. $\frac{(n+1)(n)}{2}$
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In a graph of $n$ vertices you can draw an edge from a vertex to $\left(n-1\right)$ vertex we will do it for n vertices so total number of edges is $n\left(n-1\right)$ now each edge is counted twice so the required maximum number of edges is $\frac{n\left(n-1\right)}{2}.$
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But the question disallows only self loops , parallel edges may be present.
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I have not considered parallel edge because it will lead to infinity which is not in option
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The correct answer is ∞, but if we assume that the graph is Simple (i.e self-loop and parallel edges are disallowed) then the ans will be (b) n(n-1)/2 .

For maximum no of edges we must have one edge for each pair of vertices.

We can select a pair out of N nodes in NC2 ways = N(N-1)/2

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Nice ..
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@debashish

For directed graph , maximum no of edges would be n^2 -n ??

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