  Ranking the spreading influence of nodes is of great importance in practice
and research. The key to ranking a node's spreading ability is to evaluate the
fraction of susceptible nodes been infected by the target node during the
outbreak, i.e., the outbreak size. In this paper, we present a dynamic Markov
process (DMP) method by integrating the Markov chain and the spreading process
to evaluate the outbreak size of the initial spreader. Following the idea of
the Markov process, this method solves the problem of nonlinear coupling by
adjusting the state transition matrix and evaluating the probability of the
susceptible node being infected by its infected neighbours. We have employed
the susceptible-infected-recovered (SIR) and susceptible-infected-susceptible
(SIS) models to test this method on real-world static and temporal networks.
Our results indicate that the DMP method could evaluate the nodes' outbreak
sizes more accurately than previous methods for both single and
multi-spreaders. Besides, it can also be employed to rank the influence of
nodes accurately during the spreading process.
