Abstract
In many complex systems, elements interact via time-varying network topologies. Recent research shows that temporal correlations in the chronological ordering of interactions crucially influence network properties and dynamical processes. How these correlations affect our ability to control systems with time-varying interactions remains unclear. In this work, we use higher-order network models to extend the framework of structural controllability to temporal networks, where the chronological ordering of interactions gives rise to time-respecting paths with non-Markovian characteristics. We study six empirical data sets and show that non-Markovian characteristics of real systems can both increase or decrease the minimum time needed to control the whole system. With both empirical data and synthetic models, we further show that spectral properties of generalisations of graph Laplacians to higher-order networks can be used to analytically capture the effect of temporal correlations on controllability. Our work highlights that (i) correlations in the chronological ordering of interactions are an important source of complexity that significantly influences the controllability of temporal networks, and (ii) higher-order network models are a powerful tool to understand the temporal-topological characteristics of empirical systems.
Highlights
Many complex systems have dynamic topologies that can be described by temporal networks [1]
With α larger than 0, long-range edges are favoured in temporal paths that connect distant nodes, and it is faster to achieve controllability of the whole system. This way, using simulation results that have been obtained based on a synthetic model, we show that the speed-up effect is limited to the (LT) dataset, but it can be observed if the long-range edges are enforced in the system
Applying structural controllability theory to six empirical data sets, we showed that temporal correlations can both increase or decrease the minimum time needed to make a system fully controllable
Summary
Many complex systems have dynamic topologies that can be described by temporal networks [1]. The causal topology of such systems, which captures how nodes can indirectly influence each other via causal paths, can be much more complex than what is expected based on the static and aggregated network alone [3,4,5] Exploring such higher-order dependencies in temporal networks, recent studies have revealed that they can crucially impact network properties like, e.g. node centralities [6, 7] or community structures [4, 8, 9], as well as dynamical processes like, e.g. epidemic spreading [4, 5], and diffusion [3, 4, 7, 10]. Our findings provide a possible explanation of why higher-order spectral properties may analytically capture the effect of temporal correlations, opening new perspectives to study controllability in temporal networks
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