  Structure of real networked systems, such as social relationship, can be
modeled as temporal networks in which each edge appears only at the prescribed
time. Understanding the structure of temporal networks requires quantifying the
importance of a temporal vertex, which is a pair of vertex index and time. In
this paper, we define two centrality measures of a temporal vertex based on the
fastest temporal paths which use the temporal vertex. The definition is free
from parameters and robust against the change in time scale on which we focus.
In addition, we can efficiently compute these centrality values for all
temporal vertices. Using the two centrality measures, we reveal that
distributions of these centrality values of real-world temporal networks are
heterogeneous. For various datasets, we also demonstrate that a majority of the
highly central temporal vertices are located within a narrow time window around
a particular time. In other words, there is a bottleneck time at which most
information sent in the temporal network passes through a small number of
temporal vertices, which suggests an important role of these temporal vertices
in spreading phenomena.
