"Empire" is a term is incredibly slippery term for historians to define. Empires are often very complex entities and trying to extrapolate some general features means there is a loss of nuance. For example, Charles Tilly came up with a serviceable definition for empire:

An empire is a large composite polity linked to a central power by indirect rule. The central power exercises some military and fiscal control in each major segment of its imperial domain, but tolerates two major elements of indirect rule: (1) retention or establishment of particular, distinct compacts for the government of each segment; and (2) exercise of power through intermediaries who enjoy considerable autonomy within their own domains in return for compliance, tribute, and military collaboration with the center.

Tilly's definition is quite flexible, but also deliberately quite vague and can be stretched too far. For example, one can use Tilly's definition to label the US's immediate postwar position in Western Europe an empire with economic agreements like Bretton Woods, institutions like NATO, and foreign aid like the Marshall Plan as a instruments of an American imperium. But nations like France, West Germany and the UK retained a significant amount of autonomy and national sovereignty and when looking at the State Department archives there is considerable consternation over their allies' independence. This is one problem with labeling state entities as empires haphazardly, once you stretch these conceptualizations too far, the term itself becomes distorted and loses its original meaning.

If you're so inclined, the German Historical Institute London held a plenary forum, Empires and Colonies with some leading imperial and colonial scholars that discusses the various historical approaches to this subject.