  In contrast to previous common wisdom that epidemic activity in heterogeneous
networks is dominated by the hubs with the largest number of connections,
recent research has pointed out the role that the innermost, dense core of the
network plays in sustaining epidemic processes. Here we show that the mechanism
responsible of spreading depends on the nature of the process. Epidemics with a
transient state are boosted by the innermost core. Contrarily, epidemics
allowing a steady state present a dual scenario, where either the hub
independently sustains activity and propagates it to the rest of the system,
or, alternatively, the innermost network core collectively turns into the
active state, maintaining it globally. In uncorrelated networks the former
mechanism dominates if the degree distribution decays with an exponent larger
than 5/2, and the latter otherwise. Topological correlations, rife in real
networks, may perturb this picture, mixing the role of both mechanisms.
