Studies on friendships in online social networks involving geographic distance have so far relied on the city location provided in users profiles. Consequently, most of the research on friendships have provided accuracy at the city level, at best, to designate a users location. This study analyzes a Twitter dataset because it provides the exact geographic distance between corresponding users. We start by introducing a strong definition of friend on Twitter (i.e., a definition of bidirectional friendship), requiring bidirectional communication. Next, we utilize geo-tagged mentions delivered by users to determine their locations, where @username is contained anywhere in the body of tweets. To provide analysis results, we first introduce a friend counting algorithm. From the fact that Twitter users are likely to post consecutive tweets in the static mode, we also introduce a two-stage distance estimation algorithm. As the first of our main contributions, we verify that the number of friends of a particular Twitter user follows a well-known power-law distribution (i.e., a Zipfs distribution or a Pareto distribution). Our study also provides the following newly-discovered friendship degree related to the issue of space: The number of friends according to distance follows a double power-law (i.e., a double Pareto law) distribution, indicating that the probability of befriending a particular Twitter user is significantly reduced beyond a certain geographic distance between users, termed the separation point. Our analysis provides concrete evidence that Twitter can be a useful platform for assigning a more accurate scalar value to the degree of friendship between two users.
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