What is a Nuclear Power?

I obviously don't know the definition of "Nuclear Power" when it is use to define nations who have nuclear weapons capability. For example, my Political Science professor stated that Israel is a nuclear power while North Korea isn't.

My understanding always came from this: A nation is labeled a nuclear power when is has been verified to have nuclear weapons. I guess the fact that Israel has never admitted to having nuclear weapons (although it is assumed to have them by a majority of analyst) while having actual data of North Korea detonating two nuclear bombs would mean that North Korea is certainly one with Israel probably being one.

For example, a recent article from the Washington Times reports how North Korea is suspected of adopting their current nuclear weaponry to include nuclear tipped missiles. The article shows how North Korea has already performed two underground nuclear tests, and how

On North Korea, the report disclosed for the first time the U.S. intelligence estimate of when Pyongyang will be able to reach the technically challenging threshold of producing a nuclear device small enough to be carried on a missile.

Concerning Israel, the Federation of American Scientists (FAS) reports:

Israel has not confirmed that it has nuclear weapons and officially maintains that it will not be the first country to introduce nuclear weapons into the Middle East. Yet the existence of Israeli nuclear weapons is a "public secret" by now due to the declassification of large numbers of formerly highly classified US government documents which show that the United States by 1975 was convinced that Israel had nuclear weapons.

Interesting. A nation which we know for certain has nuclear weapons is not labeled as a "nuclear power," while a nation that still has not yet admitted to having them is labeled as such.

Thanks for clearing that up for your class, professor! It's amazing how much the leftists in college love Israel and are always trying give the nation such glowing praise!