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Ranking influential spreaders is an ill-defined problem
Gu, Jain,Lee, Sungmin,Saramä,ki, Jari,Holme, Petter IOP Publishing - Europhysics Letters 2017 Europhysics letters Vol.118 No.6
<P>Finding influential spreaders of information and disease in networks is an important theoretical problem, and one of considerable recent interest. It has been almost exclusively formulated as a node-ranking problem - methods for identifying influential spreaders output a ranking of the nodes. In this work, we show that such a greedy heuristic does not necessarily work: the set of most influential nodes depends on the number of nodes in the set. Therefore, the set of n most important nodes to vaccinate does not need to have any node in common with the set of n + 1 most important nodes. We propose a method for quantifying the extent and impact of this phenomenon. By this method, we show that it is a common phenomenon in both empirical and model networks. Copyright (C) EPLA, 2017</P>