  Identifying important nodes in complex networks is a fundamental problem in
network analysis. Although a plethora of measures has been proposed to identify
important nodes in static (i.e., time-invariant) networks, there is a lack of
tools in the context of temporal networks (i.e., networks whose connectivity
dynamically changes over time). The aim of this paper is to propose a
system-theoretic approach for identifying important nodes in temporal networks.
In this direction, we first propose a generalization of the popular Katz
centrality measure to the family of Markovian temporal networks using tools
from the theory of Markov jump linear systems. We then show that Katz
centrality in Markovian temporal networks can be efficiently computed using
linear programming. Finally, we propose a convex program for optimizing the
Katz centrality of a given node by tuning the weights of the temporal network
in a cost-efficient manner. Numerical simulations illustrate the effectiveness
of the obtained results.
