  The identification of the most influential spreaders in networks is important
to control and understand the spreading capabilities of the system as well as
to ensure an efficient information diffusion such as in rumor-like dynamics.
Recent works have suggested that the identification of influential spreaders is
not independent of the dynamics being studied. For instance, the key disease
spreaders might not necessarily be so when it comes to analyze social contagion
or rumor propagation. Additionally, it has been shown that different metrics
(degree, coreness, etc) might identify different influential nodes even for the
same dynamical processes with diverse degree of accuracy. In this paper, we
investigate how nine centrality measures correlate with the disease and rumor
spreading capabilities of the nodes that made up different synthetic and
real-world (both spatial and non-spatial) networks. We also propose a
generalization of the random walk accessibility as a new centrality measure and
derive analytical expressions for the latter measure for simple network
configurations. Our results show that for non-spatial networks, the $k$-core
and degree centralities are most correlated to epidemic spreading, whereas the
average neighborhood degree, the closeness centrality and accessibility are
most related to rumor dynamics. On the contrary, for spatial networks, the
accessibility measure outperforms the rest of centrality metrics in almost all
cases regardless of the kind of dynamics considered. Therefore, an important
consequence of our analysis is that previous studies performed in synthetic
random networks cannot be generalized to the case of spatial networks.
