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arXiv · 1703.05644

Ranking influential spreaders is an ill-defined problem

Jain Gu·Sungmin Lee·Jari Saramäki·Petter Holme
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Abstract

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 rank nodes according to how influential they are. In this work, we show that the ranking approach 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, and show that it is common in both empirical and model networks.

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Jain Gu, Sungmin Lee, Jari Saramäki, Petter Holme. 2017-03-16. Ranking influential spreaders is an ill-defined problem. https://doi.org/10.1209/0295-5075/118/68002

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