Alain Barrat

Modeling temporal networks using random itineraries


Thanks to advanced acquisition technologies and large scale production of time-resolved data, temporal information has become more accessible in numerous network datasets, stimulating the studies of temporal networks. Strong limitations perdure however. Indeed, data are often only accessible in restricted forms, such as single samples of limited sizes and statistical relevance. Moreover, comparison of connection patterns in the same system but at different times is not always possible. Some datasets only consist of aggregated information and do not provide access to the temporal course of events. In such circumstances, it is of interest to be able to generate synthetic time-extended structures whose aggregation would reproduce the data at hand. This would enable one to go beyond the approximation of static networks by incorporating dynamical components in network structures, and to study the effect of various dynamical properties of the network on dynamical processes taking place on it. In this context, we propose a procedure to generate plausible and realistic instances of temporal networks, with bursty, possibly repetitive and correlated temporal behaviors, corresponding to a given temporally aggregated structure. Regarding any weighted directed graph as being composed of the accumulation of paths between its nodes, our construction uses random walks of variable length to produce time-extended structures with adjustable features. The procedure is first described in a general framework. It is then illustrated in a case study inspired by a transportation system for which the resulting synthetic network is shown to accurately mimic the empirical phenomenology.