The dynamic importance of nodes is poorly predicted by static network features

Abstract: One of the most central questions in network science is: which nodes are most important? Often this question is answered using structural properties such as high connectedness or centrality in the network. However, static structural connectedness does not necessarily translate to dynamical importance. To demonstrate this, we simulate the kinetic Ising spin model on generated networks and one real-world weighted network. The dynamic impact of nodes is assessed by causally intervening on node state probabilities and measuring the effect on the systemic dynamics. The results show that structural features such as network centrality or connectedness are actually poor predictors of the dynamical impact of a node on the rest of the network. A solution is offered in the form of an information theoretical measure named integrated mutual information. The metric is able to accurately predict the dynamically most important node ('driver' node) in networks based on observational data of non-intervened dynamics. We conclude that the driver node(s) in networks are not necessarily the most well-connected or central nodes. Indeed, the common assumption of network structural features being proportional to dynamical importance is false. Consequently, great care should be taken when deriving dynamical importance from network data alone. These results highlight the need for novel inference methods that take both structure and dynamics into account.