BFS using Adjacency Matrix

What is the running time of BFS if we represent its input graph by an
adjacency matrix and modify the algorithm to handle this form of input?

I feel if the graph is represented by adjacency matrix, then the time of iterating all the edge becomes O(V^2), so the running time is O(V+V^2).

But I read online that each vertex can be explored once and its adjacent vertices must be determined too. This takes Theta(V^2) time. And now I am confused.
How can we bound the lower limit as well?

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If you do it naively then it is O(v3)\mathcal O(v^3) time for the complete graph.
– Jorge Fernández Hidalgo
2 days ago

  

 

@JorgeFernándezHidalgo sorry I did not get you. how come?
– Harshit
2 days ago

  

 

Nevermind, I got confused , you have O(v2)\mathcal O (v^2) complexity
– Jorge Fernández Hidalgo
2 days ago

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