  In the study of disease spreading on empirical complex networks in SIR model,
initially infected nodes can be ranked according to some measure of their
epidemic impact. The highest ranked nodes, also referred to as
"superspreaders", are associated to dominant epidemic risks and therefore
deserve special attention. In simulations on studied empirical complex
networks, it is shown that the ranking depends on the dynamical regime of the
disease spreading. A possible mechanism leading to this dependence is
illustrated in an analytically tractable example. In systems where the
allocation of resources to counter disease spreading to individual nodes is
based on their ranking, the dynamical regime of disease spreading is frequently
not known before the outbreak of the disease. Therefore, we introduce a
quantity called epidemic centrality as an average over all relevant regimes of
disease spreading as a basis of the ranking. A recently introduced concept of
phase diagram of epidemic spreading is used as a framework in which several
types of averaging are studied. The epidemic centrality is compared to
structural properties of nodes such as node degree, k-cores and betweenness.
There is a growing trend of epidemic centrality with degree and k-cores values,
but the variation of epidemic centrality is much smaller than the variation of
degree or k-cores value. It is found that the epidemic centrality of the
structurally peripheral nodes is of the same order of magnitude as the epidemic
centrality of the structurally central nodes. The implications of these
findings for the distributions of resources to counter disease spreading are
discussed.
