  Identification of influential nodes is an important step in understanding and
controlling the dynamics of information, traffic and spreading processes in
networks. As a result, a number of centrality measures have been proposed and
used across different application domains. At the heart of many of these
measures, lies an assumption describing the manner in which traffic (of
information, social actors, particles, etc.) flows through the network. For
example, some measures only count shortest paths while others consider random
walks.
  This paper considers a spreading process in which a resource necessary for
transit is partially consumed along the way while being refilled at special
nodes on the network. Examples include fuel consumption of vehicles together
with refueling stations, information loss during dissemination with error
correcting nodes, and consumption of ammunition of military troops while
moving.
  We propose generalizations of the well-known measures of betweenness, random
walk betweenness, and Katz centralities to take such a spreading process with
consumable resources into account. In order to validate the results,
experiments on real-world networks are carried out by developing simulations
based on well-known models such as Susceptible-Infected-Recovered and
congestion with respect to particle hopping from vehicular flow theory. The
simulation-based models are shown to be highly correlated to the proposed
centrality measures.
