Dynamic importance of network nodes is poorly predicted by static structural features

https://doi.org/10.1016/j.physa.2022.126889Get rights and content
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Highlights

  • Driver-node identification through novel metric model-free metric: integrated mutual information.

  • Validation through causal interventions

  • For non-equilibrium dynamics structural features are not predictive for unperturbed system dynamics

  • Discusses the implicit dynamical assumptions behind many centrality measures

  • Highlights the importance of form-function relations in complex systems

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.

Keywords

Complex system
Information theory
Driver-node identification

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