Anti-preferential Attachment: If I Follow You, Will You Follow Me?

A common question in social networking research is how edges form to produce social graphs with the common characteristics, including a power-law degree distribution and a small diameter. One common model for edge formation in synthetic networks is preferential attachment. We examine the edge formation process of one Online Social Network (OSN), Buzz net, and look for evidence for preferential attachment. To our surprise, we find that a form of` `anti-preferential attachment´´ is common, in which high-degree nodes add edges to low-degree nodes, perhaps as a means of self-promotion. We also find that nodes are most likely to reciprocate edges from low-degree nodes, limiting the extent to which anti-preferential attachment can succeed in boosting a high-degree node´s in-degree.