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


One of the most central questions in network science is: which nodes are most important? Often this question is answered using topological properties such as high connectedness or centrality in the network. However it is unclear whether topological connectedness translates directly to dynamical impact. To this end, we simulate the kinetic Ising spin model on generated and a real-world networks with weighted edges. The extent of the dynamic impact is assessed by causally intervening on a node state and effect on the systemic dynamics. The results show that topological 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 information impact. The metric is able to accurately reflect dynamic importance of nodes in networks under natural dynamics using observations only, and validated using causal interventions. We conclude that the most dynamically impactful nodes are usually not the most well-connected or central nodes. This implies that the common assumption of topologically central or well-connected nodes being also dynamically important is actually false, and abstracting away the dynamics from a network before analyzing is not advised.