Abstract
In many social and biological networks, the collective dynamics of the entire system can be shaped by a small set of influential units through a global cascading process, manifested by an abrupt first-order transition in dynamical behaviors. Despite its importance in applications, efficient identification of multiple influential spreaders in cascading processes still remains a challenging task for large-scale networks. Here we address this issue by exploring the collective influence in general threshold models of cascading process. 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 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 the same number of seeds compared with other scalable heuristic approaches.
Highlights
Treated with the stability analysis methods based on the non-backtracking matrix as done in15,16 for models with continuous transitions, so a new approach is needed
The cascading dynamics of Linear Threshold Model (LTM) can be mapped to the classical percolation process15, for which the influence maximization problem can be solved by various algorithms designed for optimal percolation
We present a theoretical framework to analyze the collective influence of individuals in general LTM
Summary
Treated with the stability analysis methods based on the non-backtracking matrix as done in for models with continuous transitions, so a new approach is needed. The choice of threshold mi = ki − 1 in LTM guarantees a continuous phase transition, where ki is the degree of node i In this case, the cascading dynamics of LTM can be mapped to the classical percolation process, for which the influence maximization problem can be solved by various algorithms designed for optimal percolation. Guggiola and Semerjian obtained the theoretical limit of the size of minimal contagious sets for random regular graphs, and used a survey propagation like algorithm to locate the minimal set of seeds Given these recent progresses in searching for optimal influencers in LTM, it is a challenging task to apply these methods to massively large-scale networks with tens of millions nodes encountered in modern big-data analysis. Compared with other competing heuristics, our results on both synthetic and realistic large-scale networks reveal that the proposed mechanism-based algorithm can produce a larger cascading process given the same number of seeds
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