text: Many dynamic networks coming from real-world contexts are link streams, i.e. a finite collection of triplets @math where @math and @math are two nodes having a link between them at time @math . A very large number of studies on these objects start by aggregating the data in disjoint time windows of length @math in order to obtain a series of graphs on which are made all subsequent analyses. Here we are concerned with the impact of the chosen @math on the obtained graph series. We address the fundamental question of knowing whether a series of graphs formed using a given @math faithfully describes the original link stream. We answer the question by showing that such dynamic networks exhibit a threshold for @math , which we call the , beyond which the properties of propagation of the link stream are altered, while they are mostly preserved before. We design an automatic method to determine the saturation scale of any link stream, which we apply and validate on several real-world datasets.
  @cite_31: We introduce a system for sensing complex social systems with data collected from 100 mobile phones over the course of 9 months. We demonstrate the ability to use standard Bluetooth-enabled mobile telephones to measure information access and use in different contexts, recognize social patterns in daily user activity, infer relationships, identify socially significant locations, and model organizational rhythms.
  @cite_22: The topology of social networks can be understood as being inherently dynamic, with edges having a distinct position in time. Most characterizations of dynamic networks discretize time by converting temporal information into a sequence of network "snapshots" for further analysis. Here we study a highly resolved data set of a dynamic proximity network of 66 individuals. We show that the topology of this network evolves over a very broad distribution of time scales, that its behavior is characterized by strong periodicities driven by external calendar cycles, and that the conversion of inherently continuous-time data into a sequence of snapshots can produce highly biased estimates of network structure. We suggest that dynamic social networks exhibit a natural time scale nat , and that the best conversion of such dynamic data to a discrete sequence of networks is done at this natural rate.
  @cite_6: The study of complex social systems has traditionally been an arduous process, involving extensive surveys, interviews, ethnographic studies, or analysis of online behavior. Today, however, it is possible to use the unprecedented amount of information generated by pervasive mobile phones to provide insights into the dynamics of both individual and group behavior. Information such as continuous proximity, location, communication and activity data, has been gathered from the phones of 100 human subjects at MIT. Systematic measurements from these 100 people over the course of eight months have generated one of the largest datasets of continuous human behavior ever collected, representing over 300,000 hours of daily activity. In this thesis we describe how this data can be used to uncover regular rules and structure in behavior of both individuals and organizations, infer relationships between subjects, verify selfreport survey data, and study social network dynamics. By combining theoretical models with rich and systematic measurements, we show it is possible to gain insight into the underlying behavior of complex social systems. Thesis Supervisor: Alex P. Pentland Title: Toshiba Professor of Media Arts and Sciences, MIT.
summary: @cite_22 also aims at determining an appropriate time scale for aggregating a link stream into a graph series. Their method does not take into account the loss of information but is instead based on the modes of periodicity and on the self-similarity of the time series of some properties of the snapshots. They observe that the offset time for which the self similarity of these time series is zero is close to half of the period of the highest frequency visible in their spectra, which is the aggregation period suggested as a result of their method. Though this provides a very relevant time scale for analyzing dynamic networks, its meaning is different from the meaning of the saturation scale we are looking for in this paper. Indeed, an important part of the activity of dynamic networks takes place at time scales much smaller than their modes of periodicity. Therefore, using such periods for aggregation usually induces an important loss of information, which we aim at avoiding here. Let us mention that a similar approach based on modes of periodicity of some time series associated to the network was previously used in @cite_6 @cite_31 .