Characterising Temporal Distance and Reachability in Mobile and Online Social Networks

The analysis of social and technological networks has attracted a lot of attention as social networking applications and mobile sensing devices have given us a wealth of real data. Classic studies looked at analysing static or aggregated networks, i.e., networks that do not change over time or built as the results of aggregation of information over a certain period of time. Given the soaring collections of measurements related to very large, real network traces, researchers are quickly starting to realise that connections are inherently varying over time and exhibit more dimensionality than static analysis can capture. In this paper we propose new temporal distance metrics to quantify and compare the speed (delay) of information diffusion processes taking into account the evolution of a network from a global view. We show how these metrics are able to capture the temporal characteristics of time-varying graphs, such as delay, duration and time order of contacts (interactions), compared to the metrics used in the past on static graphs. We also characterise network reachability with the concepts of in-and out-components. Then, we generalise them with a global perspective by defining temporal connected components. As a proof of concept we apply these techniques to two classes of time-varying networks, namely connectivity of mobile devices and interactions on an online social network.