It means that the in a connected graph the no. of vertices can never exceed the no. of edges because minimum edges in a connected graph of $n$ nodes will be $O(n)$ and maximum no of edges will be $O(n^2)$

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How to understand this: For a connected graph, V = O(E))

SOURCE http://www.geeksforgeeks.org/greedy-algorithms-set-5-prims-mst-for-adjacency-list-representation/

prims algorithm time complexity for adjacency list representation. Also same is given in CLRS but no reason

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