If complete graph have ‘n’ nodes, then it will have how many edges?

2021

If complete graph have ‘n’ nodes, then it will have how many edges?

  1. A.

    n(n-1)/2

  2. B.

    (n-1)/2

  3. C.

    n/2

  4. D.

    n(n-1)/4

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Show answer & explanation

Correct answer: A

In a complete graph with n nodes, every node is connected to every other node exactly once.

Step 1: Each node connects to (n-1) other nodes.

Step 2: The total number of connections, if counted from each node, is n(n-1).

Step 3: However, each edge is counted twice (once from each endpoint), so we divide by 2.

Step 4: The total number of unique edges is n(n-1)/2.

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