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Big data open up unprecedented opportunities to investigate complex systemsincluding the society. In particular, communication data serve as major sourcesfor computational social sciences but they have to be cleaned and filtered asthey may contain spurious information due to recording errors as well asinteractions, like commercial and marketing activities, not directly related tothe social network. The network constructed from communication data can only beconsidered as a proxy for the network of social relationships. Here we apply asystematic method, based on multiple hypothesis testing, to statisticallyvalidate the links and then construct the corresponding Bonferroni network,generalized to the directed case. We study two large datasets of mobile phonerecords, one from Europe and the other from China. For both datasets we comparethe raw data networks with the corresponding Bonferroni networks and point outsignificant differences in the structures and in the basic network measures. Weshow evidence that the Bonferroni network provides a better proxy for thenetwork of social interactions than the original one. By using the filterednetworks we investigated the statistics and temporal evolution of smalldirected 3-motifs and conclude that closed communication triads have aformation time-scale, which is quite fast and typically intraday. We also findthat open communication triads preferentially evolve to other open triads witha higher fraction of reciprocated calls. These stylized facts were observed forboth datasets.

Statistically validated mobile communication networks: Evolution of motifs in European and Chinese data