  Networks are well-established representations of social systems, and temporal
networks are widely used to study their dynamics. Temporal network data often
consist in a succession of static networks over consecutive time windows whose
length, however, is arbitrary, not necessarily corresponding to any intrinsic
timescale of the system. Moreover, the resulting view of social network
evolution is unsatisfactory: short time windows contain little information,
whereas aggregating over large time windows blurs the dynamics. Going from a
temporal network to a meaningful evolving representation of a social network
therefore remains a challenge. Here we introduce a framework to that purpose:
transforming temporal network data into an evolving weighted network where the
weights of the links between individuals are updated at every interaction. Most
importantly, this transformation takes into account the interdependence of
social relationships due to the finite attention capacities of individuals:
each interaction between two individuals not only reinforces their mutual
relationship but also weakens their relationships with others. We study a
concrete example of such a transformation and apply it to several data sets of
social interactions. Using temporal contact data collected in schools, we show
how our framework highlights specificities in their structure and temporal
organization. We then introduce a synthetic perturbation into a data set of
interactions in a group of baboons to show that it is possible to detect a
perturbation in a social group on a wide range of timescales and parameters.
Our framework brings new perspectives to the analysis of temporal social
networks.
