On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Proceedings of the 9th international World Wide Web conference on Computer networks : the international journal of computer and telecommunications netowrking
The "DGX" distribution for mining massive, skewed data
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
On the structural properties of massive telecom call graphs: findings and implications
CIKM '06 Proceedings of the 15th ACM international conference on Information and knowledge management
A framework for community identification in dynamic social networks
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Mobile call graphs: beyond power-law and lognormal distributions
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
A visual-analytic toolkit for dynamic interaction graphs
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Scalable graph clustering using stochastic flows: applications to community discovery
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Power-Law Distributions in Empirical Data
SIAM Review
Modeling relationship strength in online social networks
Proceedings of the 19th international conference on World wide web
Surprising patterns for the call duration distribution of mobile phone users
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part III
Clustering Social Networks Using Distance-Preserving Subgraphs
ASONAM '10 Proceedings of the 2010 International Conference on Advances in Social Networks Analysis and Mining
The self-feeding process: a unifying model for communication dynamics in the web
Proceedings of the 22nd international conference on World Wide Web
Dynamics of trust reciprocation in multi-relational networks
Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
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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.