The current exploratory study examines the trajectory of individuals’ friendship formation in the online social network. Specifically, this study started with the anthropological data mining in order to learn the basic pattern of individuals’ online friendship formation. Then we explored the time path of the friendship formation by regressing the cumulative number of friends on time using polynomial logistic function. Interestingly, we found the increase of number of friends within each user typically follows a logistic function with time, indicating that the growth rate of number of friends for each user might slowly increase and then decrease. More importantly, the trajectories appear uniformly, if not identically, across individuals. Our findings contrast with the two dominant assumptions which claim that (1) users create a first edge, and never come back; (2) the level of number of friend addition seems to be uniform over time. Regarding the saturation time point of the friendship growth, we have found that it takes on average 290 days for individuals to build up their personal connections online. More surprisingly, we found a self-similar trajectory of growth of friendship between individual and global level.

Major Findings

1. Distribution of R-squares of Polynomial Logistic Modeling.

2. Distribution of Saturation Points (percent)

3. Distribution of Saturation Points (day)

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