Where does the Milky Way end? I was reading this article
 and it says the following:


  Researchers measured the mass of the Milky Way and found that our galaxy is approximately half the weight of a neighbouring galaxy known as Andromeda which has a similar structure to our own. 


So I was thinking, if we consider a galaxy neighbor to us, then our galaxy should be having an endpoint and the neighboring galaxy should be having a start point. So how do we know which is the starting and ending point of a galaxy, and how do we calculate it?
Here's a rough sketch of the Milky Way and the Andromeda galaxy,* showing their approximate sizes and distance from each other to scale:

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What the picture (hopefully) illustrates is the incredibly vast gap of empty space &mdash; around 2.5 million light years, to be exact &mdash; between the galaxies, each of which has a diameter of only(!) around 100 thousand light years or so.

While both galaxies are shaped pretty much like "fuzzy whirlpools" of dust and gas (and, apparently, dark matter), with no precisely defined sharp outer edge, they are still pretty unambiguously separated.  While we may not be able to point to a specific line in space and say that "the Milky Way ends right here", it's still clear that the Milky Way is over here, while the Andromeda galaxy is over there, and there's a huge gap of pretty much absolutely nothing at all in between.

(Of course, there is some stuff even in intergalactic space, including some very diffuse gas, a little bit of dust and even the occasional stray star.  Still, compared to the galaxies themselves &mdash; which, from a human viewpoint, are already pretty full of empty space &mdash; the intergalactic medium can be pretty well described as empty.)

*) The little specks in the picture around each major galaxy are meant to represent their smaller satellite galaxies, such as the lesser and greater Magellanic clouds. Their relative positions and distances, alas, are probably not very accurate.