Weighted reciprocity in human communication networks
  In this paper we define a metric for reciprocity---the degree of balance in a social relationship---appropriate for weighted social networks in order to investigate the distribution of this dyadic feature in a large-scale system built from trace-logs of over a billion cell-phone communication events across millions of actors. We find that dyadic relations in this network are characterized by much larger degrees of imbalance than we would expect if persons kept only those relationships that exhibited close to full reciprocity. We point to two structural features of human communication behavior and relationship formation---the division of contacts into strong and weak ties and the tendency to form relationships with similar others---that either help or hinder the ability of persons to obtain communicative balance in their relationships. We examine the extent to which deviations from reciprocity in the observed network are partially traceable to these characteristics. 
Cheng Wang and Anthony Strathman and Omar Lizardo and David Hachen and   Zoltan Toroczkai and Nitesh V. Chawla
cs.SI physics.soc-ph