  Reciprocity in directed networks points to user's willingness to return
favors in building mutual interactions. High reciprocity has been widely
observed in many directed social media networks such as following relations in
Twitter and Tumblr. Therefore, reciprocal relations between users are often
regarded as a basic mechanism to create stable social ties and play a crucial
role in the formation and evolution of networks. Each reciprocity relation is
formed by two parasocial links in a back-and-forth manner with a time delay.
Hence, understanding the delay can help us gain better insights into the
underlying mechanisms of network dynamics. Meanwhile, the accurate prediction
of delay has practical implications in advancing a variety of real-world
applications such as friend recommendation and marketing campaign. For example,
by knowing when will users follow back, service providers can focus on the
users with a potential long reciprocal delay for effective targeted marketing.
This paper presents the initial investigation of the time delay in reciprocal
relations. Our study is based on a large-scale directed network from Tumblr
that consists of 62.8 million users and 3.1 billion user following relations
with a timespan of multiple years (from 31 Oct 2007 to 24 Jul 2013). We reveal
a number of interesting patterns about the delay that motivate the development
of a principled learning model to predict the delay in reciprocal relations.
Experimental results on the above mentioned dynamic networks corroborate the
effectiveness of the proposed delay prediction model.
