Collective influence maximization in threshold models of information cascading with first-order transitions

In spreading dynamics in social networks, there exists an optimal set of influencers whose activation can induce a global-scale cascade of information. To find the optimal, or minimal, set of spreaders, a method based on collective influence theory has been proposed for spreading dynamics with a continuous phase transition that can be mapped to optimal percolation. However, when it comes to diffusion processes exhibiting a first-order, or discontinuous transition, identifying the set of optimal spreaders with a linear algorithm for large-scale networks still remains a challenging task. Here we address this issue by exploring the collective influence in general threshold models of opinion 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 set of spreaders predicted by our method is smaller than those identified by other linearly scalable heuristic approaches.

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