Networks are commonly used to define underlying interaction structures where infections, information, or other quantities may spread. Although the standard approach has been to aggregate all links into a static structure, some studies have shown that the time order in which the links are established may alter the dynamics of spreading. In this paper, we study the impact of the time ordering in the limits of flow on various empirical temporal networks. By using a random walk dynamics, we estimate the flow on links and convert the original undirected network (temporal and static) into a directed flow network. We then introduce the concept of flow motifs and quantify the divergence in the representativity of motifs when using the temporal and static frameworks. We find that the regularity of contacts and persistence of vertices (common in email communication and face-to-face interactions) result on little differences in the limits of flow for both frameworks. On the other hand, in the case of communication within a dating site and of a sexual network, the flow between vertices changes significantly in the temporal framework such that the static approximation poorly represents the structure of contacts. We have also observed that cliques with 3 and 4 vertices containing only low-flow links are more represented than the same cliques with all high-flow links. The representativity of these low-flow cliques is higher in the temporal framework. Our results suggest that the flow between vertices connected in cliques depend on the topological context in which they are placed and in the time sequence in which the links are established. The structure of the clique alone does not completely characterize the potential of flow between the vertices.
Flow motifs reveal limitations of the static framework to represent human interactions
Luis E. C. Rocha and Vincent D. Blondel
Phys. Rev. E 87, 042814 (2013)