  In social networks, the collective behavior of large populations can be
shaped by a small set of influencers through a cascading process induced by
"peer pressure". For large-scale networks, efficient identification of multiple
influential spreaders with a linear algorithm in threshold models that exhibit
a first-order transition still remains a challenging task. Here we address this
issue by exploring the collective influence in general threshold models of
behavior cascading. Our analysis reveals that the importance of spreaders is
fixed by the subcritical paths along which cascades propagate: the number of
subcritical paths attached to each spreader determines its contribution to
global cascades. The concept of subcritical path allows us to introduce a
linearly scalable algorithm for massively large-scale networks. Results in both
synthetic random graphs and real networks show that the proposed method can
achieve larger collective influence given same number of seeds compared with
other linearly scalable heuristic approaches.
