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Phys Rev E. 2017 Dec;96(6-1):062305. doi: 10.1103/PhysRevE.96.062305. Epub 2017 Dec 5.

Three faces of node importance in network epidemiology: Exact results for small graphs.

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Institute of Innovative Research, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku Yokohama, Kanagawa 226-8503, Japan.


We investigate three aspects of the importance of nodes with respect to susceptible-infectious-removed (SIR) disease dynamics: influence maximization (the expected outbreak size given a set of seed nodes), the effect of vaccination (how much deleting nodes would reduce the expected outbreak size), and sentinel surveillance (how early an outbreak could be detected with sensors at a set of nodes). We calculate the exact expressions of these quantities, as functions of the SIR parameters, for all connected graphs of three to seven nodes. We obtain the smallest graphs where the optimal node sets are not overlapping. We find that (i) node separation is more important than centrality for more than one active node, (ii) vaccination and influence maximization are the most different aspects of importance, and (iii) the three aspects are more similar when the infection rate is low.


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