What you do with the hot neighbor across the street when the husband or wife is away/gone/out of picture or just at work. You are not dating, in a relationship, or any other defined word other than neighboring. It is a hush hush thing where you sneak in and out after the kids are asleep to avoid a scandal on your block. No public displays of affection are allowed, otherwise it would not easily stay with in the confines of the word neighboring. What happens behind closed doors, stays behind closed doors. No matter what she tells her twin sister/brother or what he or she wants to call it, it is just neighboring and that is that. Every other weekend when the kids are with the baby daddy/baby mama they can have little adventures such as a weekend trip to Miami but that STILL doesn't change anything. You are still just neighbors in a different geological location. Neighboring specifically refers to the process of this behavior. It is possible to be involved with neighboring more than one neighbor or several of those in the neighborhood if you all continue to call each other neighbors. If you want to get cute you can call each other Nei Nei and that will be another word to define here in the Urban Dictionary.
I am going out to Walmart to do some neighboring with my Nei Nei, we might spend a little time in the changing room, then come back to the house and "Watch a Movie."