Clarifying the Role of Distance in Friendships on Twitter: Discovery of a Double Power-Law Relationship

TL;DR

This paper investigates how geographic distance influences Twitter friendships, revealing a double power-law distribution that describes the probability of forming friendships at various distances, offering a nuanced understanding of spatial social ties.

Contribution

It introduces a novel two-stage distance estimation algorithm and discovers a double power-law relationship in Twitter friendships based on geographic distance, refining previous homogeneous models.

Findings

Friendship probability decreases sharply beyond a certain distance.

Friendship distribution follows a double power-law, not a single one.

Provides a more detailed spatial analysis of online social ties.

Abstract

This study analyzes friendships in online social networks involving geographic distance with a geo-referenced Twitter dataset, which provides the exact distance between corresponding users. We start by introducing a strong definition of "friend" on Twitter, requiring bidirectional communication. Next, by utilizing geo-tagged mentions delivered by users to determine their locations, we introduce a two-stage distance estimation algorithm. As our main contribution, our study 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 much more fine-grained social ties in space, compared to the conventional results showing a homogeneous power-law with distance.