Can't you accept them to be both European and Asian? *Lunatic*, n. One whose delusions are out of fashion.
By the way, famously neutral Switzerland is not in the EU, nor do I think it is ever likely to be, but it is definitely in Europe. So... guaranteed to evoke a violent reaction from police is to challenge their right to "define the situation." --- David Graeber citing Marc Cooper
For me, Europe is a geographical term more than anything else. The excerpt above that starts with "Geographically Europe is a part of..." best describes Europe as such.
This is true for me too - and when I read "center of Europe", I can only think of the geographical sense of "Europe". BTW, the Southeastern geographical border ambiguities shan't change the center much - the Caucasus Mountains - Kura river difference is only a 100 km wide strip, the Ural-Emba rivers idfference is roughly 500 km x 500 km, altogether a difference of 0.33 million km² - in a 10 million km² area.
You can visualise it on another relevant map from the Wiki article (here the Emba and Kura rivers are the borders; Georgia's and Azerbaijan's northern border is the Caucasus Mountains, the Ural river follows Russian-Kazakh border half-way East and then turns South):
II Europe, according to one commonly-reckoned definition II Extension over Asia of the continuous territory of a European state II Geographically in Asia, considered European for cultural and historical reasons *Lunatic*, n. One whose delusions are out of fashion.
It's insanity, I tell ya. Those who can make you believe absurdities can make you commit atrocities. -Voltaire
If you overlay a general map of Eurasia with the specific types of maps above you would get broad pattern of agreement in-though not complete or perfect alignment by any means with-the general notion of Europe. That would just be a starting point for the more significant question, which I think that you are asking, which is, who are you people who live in this large area? Is there a set of commonalities between you that differentiate you in important ways from those of us who do not live there? If there is a set of commonalities is it a result of facts on the ground, or is it an outlook based on ideas?
From across the Atlantic, it looks more and more that an European identity is coming into being, again. From afar it appears that the history, the political organizations, and the economics are being expressed with a sufficient cohesion to at least superficially express a specific and identifiable grouping of people. In the dark hour we are going through here, we hope both that people can see all the things that we have in common that are not expressed on these maps, and that Europe, whatever it is, stands for enlightenment. "I said, 'Wait a minute, Chester, You know I'm a peaceful man...'" Robbie Robertson
You will really learn to love all the info that can be mapped, and how it all integrates with econ, history, politics, etc.
Good luck on the journey. "I said, 'Wait a minute, Chester, You know I'm a peaceful man...'" Robbie Robertson