Networks are well-established tools to represent social systems, and, thanks to the increased availability of temporally resolved data, temporal networks are now widely used to model their dynamics. Temporal network data are usually presented as a succession of point events (if the data is in continuous time), or as a series of static snapshots networks aggregated on successive time windows. In the latter case, the time window length is arbitrary and does not necessarily correspond to any intrinsic timescale. Short time windows contain little information on the underlying system at each time, while long time windows provide a blurred image of the dynamics. An interesting alternative consists then in transforming the temporal network data into a continuously evolving representation that gives at any time a sensible image of the social system under study. Here we introduce such a representation that maps temporal network data of discretized dyadic interactions into an evolving weighted network in which the weights of the links between individuals are updated at every event of the temporal network. The starting point of this representation is the assumption that each individual has a limited capital of "attention" or available time: as a result, if individual i has an interaction with a peer j, the weight of the tie between i and j strengthens while the weight of the ties between i and other peers decreases. The rate of increase or decrease of weights depends on a parameter a that determines the sensitivity of this representation to changes in the underlying interaction dynamics. To show the interest of our framework, we consider several temporal data sets describing interactions (i) in a group of baboons (ii) among humans, and we simulate a change in the group's social structure by switching the identity of 2 individuals in the data at a time t0. We then consider the capacity of three representations of the data to automatically detect the perturbation: (i) a time aggregation from the initial time to t (ii) a time-aggregation at a daily scale (iii) our framework. We show that the procedure of comparing the representations at all pairs of times (t, t') and hierarchically clustering times allows us to recover t0 in all cases, but with a better performance (as measured by the quality factor of the hierarchical clustering) on a broad range of values of a for the proposed representation. This shows that our representation is well suited to the detection of significant events in the network evolution.
