Hub-betweenness analysis in delay tolerant networks inferred by real traces

In this paper we study the influence of using hub nodes to relay messages in human-based delay tolerant networks (DTNs), by analyzing empirical traces obtained by human mobility monitoring experiments. Four traces known in literature have been considered. We exploit a measure of centrality (or betweenness) over underlying graphs associated to temporal networks, in order to establish (in probability) the ability to forward information using a restricted number of active relay nodes (hubs). The proposed analyses are carried out by introducing time-dependent networks associated to real traces. The empirical cumulative distribution of the node betweenness and the shortest paths length (or geodetic) are derived and characterized. The analysis shows that the geodetic path length follows a lognormal (skewed) distribution. It is also observed that the measures of betweenness on the nodes, if ordered decreasingly and interpreted as probability distribution, exhibit an exponential-like decay, with very high betweenness for few nodes and much lower for all the others. Based on this knowledge, we study the probability of successful delivery when a set of nodes with low betweenness are deactivated as forwarding nodes. Under these assumptions, we give the probability that a k-length path connecting an arbitrary source-destination pair belong to the set of the activated hub nodes. The results show how a trade-off can be found between the number of relay nodes (hubs) activated in a temporal network and the network's delivery rate, when message forwarding is allowed only for these hubs.