Abstract
Identifying key agents for the transmission of diseases (ideas, technology, etc.) across social networks has predominantly relied on measures of centrality on a static base network or a temporally flattened graph of agent interactions. Various measures have been proposed as the best trackers of influence, such as degree centrality, betweenness, and k-shell, depending on the structure of the connectivity. We consider SIR and SIS propagation dynamics on a temporally-extruded network of observed interactions and measure the conditional marginal spread as the change in the magnitude of the infection given the removal of each agent at each time: its temporal knockout (TKO) score. We argue that this TKO score is an effective benchmark measure for evaluating the accuracy of other, often more practical, measures of influence. We find that none of the network measures applied to the induced flat graphs are accurate predictors of network propagation influence on the systems studied; however, temporal networks and the TKO measure provide the requisite targets for the search for effective predictive measures.
Highlights
Identifying key agents for the transmission of diseases across social networks has predominantly relied on measures of centrality on a static base network or a temporally flattened graph of agent interactions
We consider SIR and SIS propagation dynamics on a temporally-extruded network of observed interactions and measure the conditional marginal spread as the change in the magnitude of the infection given the removal of each agent at each time: its temporal knockout (TKO) score
We find that none of the network measures applied to the induced flat graphs are accurate predictors of network propagation influence on the systems studied; temporal networks and the TKO measure provide the requisite targets for the search for effective predictive measures
Summary
Aaron Bramson1,2,3 & Benjamin Vandermarliere[2,4] received: 18 April 2016 accepted: 05 September 2016 Published: 27 September 2016. We consider SIR and SIS propagation dynamics on a temporally-extruded network of observed interactions and measure the conditional marginal spread as the change in the magnitude of the infection given the removal of each agent at each time: its temporal knockout (TKO) score. Our analysis proceeds through the following steps: (1) create collections of scale-free and small world base networks; (2) build temporal webs encapsulating a fixed set of potential interactions for each one; (3) simulate propagation dynamics across each temporal web for each agent of each network; (4) calculate the temporal knockout of each node in the temporal web; (5) generate the flattened network and analyze the flat networks using centrality measures; (6) examine the degree to which the flat network measures capture the agents influence as measured by TKO.
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