All of the "classical empires" began as river civilizations. From the beggining of time, mankind roamed about looking for food as a group of small hunter gatherer societies. That said, with the coming of the agricultural revolution, man began to settle in places that had the best, most fertile soil... this of course being around the river valleys such as the Indus in ancient India, the Tigris and Euphrates in ancient Mesopotamia (today the area of Iraq) and probably the best example of the Nile in ancient Egypt. In short, all of these civilizations grew into the empires that you're speaking of because they had the necessary component to life, water. In the case of Rome and Greece, farming around rivers like the Tiber became grand enough for the civilizations to begin moving out and conquering more and more territory. The same can be said for the ancient empires in China and India as well.