Recent research on temporal networks has highlighted the limitations of a
static network perspective for our understanding of complex systems with
dynamic topologies. In particular, recent works have shown that i) the specific
order in which links occur in real-world temporal networks affects causality
structures and thus the evolution of dynamical processes, and ii) higher-order
aggregate representations of temporal networks can be used to analytically
study the effect of these order correlations on dynamical processes. In this
article we analyze the effect of order correlations on path-based centrality
measures in real-world temporal networks. Analyzing temporal equivalents of
betweenness, closeness and reach centrality in six empirical temporal networks,
we first show that an analysis of the commonly used static, time-aggregated
representation can give misleading results about the actual importance of
nodes. We further study higher-order time-aggregated networks, a recently
proposed generalization of the commonly applied static, time-aggregated
representation of temporal networks. Here, we particularly define path-based
centrality measures based on second-order aggregate networks, empirically
validating that node centralities calculated in this way better capture the
true temporal centralities of nodes than node centralities calculated based on
the commonly used static (first-order) representation. Apart from providing a
simple and practical method for the approximation of path-based centralities in
temporal networks, our results highlight interesting perspectives for the use
of higher-order aggregate networks in the analysis of time-stamped network
data.Comment: 27 pages, 13 figures, 3 table