Other forms: contiguities
Use the noun contiguity when you're talking about the state of things being right up next to each other, like the contiguity of two countries that share a border.
You're most likely to come across the word contiguity in a discussion of geography. For example, you could talk about the contiguity of the United States and its northern neighbor, Canada, or the contiguity of New Hampshire and Vermont. Contiguity shares a root with the more common contiguous, the Latin contingere, which means "to touch upon."