**Abstract**

Temporal networks are graphs in which edges have temporal labels, specifying their

starting times and their traversal times. Several notions of distances between two nodes in a temporal

network can be analyzed, by referring, for example, to the earliest arrival time or to the latest starting

time of a temporal path connecting the two nodes. In this paper we mostly refer to the notion of

temporal reachability by using the earliest arrival time. In particular, we first show how the sketch

approach, which has been already used in the case of classical graphs, can be applied to the case of

temporal networks in order to approximately compute the sizes of the temporal cones of a temporal

network. By making use of this approach, we subsequently show how we can approximate the

temporal neighborhood function (that is, the number of pairs of nodes reachable from one another in

a given time interval) of large temporal networks in a few seconds. Finally, we apply our algorithm

in order to analyze and compare the behavior of 25 public transportation temporal networks. Our

results can be easily adapted to the case in which we want to refer to the notion of distance based on

the latest starting time.