Quantifying Reciprocity in Large Weighted Communication Networks

  • Leman Akoglu
  • Pedro O. S. Vaz de Melo
  • Christos Faloutsos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7302)


If a friend called you 50 times last month, how many times did you call him back? Does the answer change if we ask about SMS, or e-mails? We want to quantify reciprocity between individuals in weighted networks, and we want to discover whether it depends on their topological features (like degree, or number of common neighbors). Here we answer these questions, by studying the call- and SMS records of millions of mobile phone users from a large city, with more than 0.5 billion phone calls and 60 million SMSs, exchanged over a period of six months. Our main contributions are: (1) We propose a novel distribution, the Triple Power Law (3PL), that fits the reciprocity behavior of all 3 datasets we study, with a better fit than older competitors, (2) 3PL is parsimonious; it has only three parameters and thus avoids over-fitting, (3) 3PL can spot anomalies, and we report the most surprising ones, in our real networks, (4) We observe that the degree of reciprocity between users is correlated with their local topological features; reciprocity is higher among mutual users with larger local network overlap and greater degree similarity.


Cumulative Distribution Function Phone Call Edge Weight Anomaly Detection Bivariate Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Leman Akoglu
    • 1
    • 3
  • Pedro O. S. Vaz de Melo
    • 2
    • 3
  • Christos Faloutsos
    • 1
    • 3
  1. 1.School of Computer ScienceCarnegie Mellon UniversityUSA
  2. 2.Universidade Federal de Minas GeraisBrazil
  3. 3.iLabHeinz CollegeUSA

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