  It is widely acknowledged that the initial spreaders play an important role
for the wide spreading of information in complex networks. Thus, a variety of
centrality-based methods have been proposed to identify the most influential
spreaders. However, most of the existing studies have overlooked the fact that
in real social networks it is more costly and difficult to convince influential
individuals to act as initial spreaders, resulting in a high risk in maximizing
the spreading. In this paper, we address this problem on the basis of the
assumption that large-degree nodes are activated with a higher risk than
small-degree nodes. We aim to identify the effective initial spreaders to
maximize spreading when considering both the activation risk and the outbreak
size of initial spreaders. On random networks, the analytical analysis reveals
that the degree of optimal initial spreaders does not correspond to the largest
degree of nodes in the network but rather be determined by infection
probability and difference of activation risk among nodes with different
degree. Here, we propose a risk-aware metric to identify the effective
spreaders on real networks. The numerical simulation shows that the risk-aware
metric outperforms the existing benchmark centralities in maximizing the
effective spreading.
