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?
- A.
n(n-1)/2
- B.
(n-1)/2
- C.
n/2
- D.
n(n-1)/4
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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.