Where had the Big Bang happened? Where is the center of the universe?

There is no center of the universe, because the universe is not originated from a “bang”. Instead of exploding like a bomb the universe is expanding like a balloon. Explosion and expansion are two different cases. In explosion the particles burst outward from where its center is, and a person standing in the way would see them coming toward him. But it is not so in case of expansion. If we take an example of a dotted balloon in context of the universe then as the balloon expands gradually no dot nears the other one. But all the dots are moving away from one another. The balloon so expanding can not have a center, because instead of exploding from a certain center point the balloon is expanding simultaneously everywhere.

Looking at the universe as such balloon it can be said that the Big Bang did not happen at some certain place, but everywhere. Hence, when seen from the Earth as it looks like the Earth is the center of the all expanding universe, same does it seem from any other place.

Additional reading:
Big Bang (Wikipedia)
Universe (Wikipedia)
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