Human Dynamics in Large Communication Networks

How often humans communicate with each other? What are the mechanisms that explain how human actions are distributed over time? Here we answer these questions by studying the time interval between calls and SMS messages in an anonymized, large mobile network, with 3.1 million users, over 200 million phone calls and 300 million SMS messages,spanning 70 GigaBytes. Our first contribution is the Truncated Autocatalytic Process (TAP ) model, that explains the time between communication events (ie., times between phone-initiations) for a single individual. The novelty is that the model is ’autocatalytic’, in the sense that the parameters of the model change, depending on the latest inter-event time: long periods of inactivity in the past result in long periods of inactivity in the future, and vice-versa. We show that the TAP model mimics the inter-event times of the users of our dataset extremely well, despite its parsimony and simplicity. Our second contribution is the TAP-classifier , a classification method based on the interevent times and in addition to other features. We showed that the inferred sleep intervals and the reciprocity between outgoing and incoming calls are good features to classify users. Finally, analyze the network effects of each class of users and we found surprising results. Moreover, all of our methods are fast, and scale linearly with the number of customers.

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