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.
Cite
@article{arxiv.1703.05644,
title = {Ranking influential spreaders is an ill-defined problem},
author = {Jain Gu and Sungmin Lee and Jari Saramäki and Petter Holme},
journal= {arXiv preprint arXiv:1703.05644},
year = {2017}
}