Abstract
Consensus and decision-making are often analysed in the context of networks, with many studies focusing attention on ranking the nodes of a network depending on their relative importance to information routing. Dynamical influence ranks the nodes with respect to their ability to influence the evolution of the associated network dynamical system. In this study it is shown that dynamical influence not only ranks the nodes, but also provides a naturally optimised distribution of effort to steer a network from one state to another. An example is provided where the “steering” refers to the physical change in velocity of self-propelled agents interacting through a network. Distinct from other works on this subject, this study looks at directed and hence more general graphs. The findings are presented with a theoretical angle, without targeting particular applications or networked systems; however, the framework and results offer parallels with biological flocks and swarms and opportunities for design of technological networks.
Highlights
Consensus and decision-making are often analysed in the context of networks, with many studies focusing attention on ranking the nodes of a network depending on their relative importance to information routing
Dynamical influence ranks the nodes with respect to their ability to influence the evolution of the associated network dynamical system
We investigated and extended the concept of dynamical influence to cover which nodes should be in charge to lead the dynamics, and how much effort they should invest in doing so
Summary
Consensus and decision-making are often analysed in the context of networks, with many studies focusing attention on ranking the nodes of a network depending on their relative importance to information routing. Algorithms, analytic proofs and empirical studies have been widely reported, shedding new light on this matter[9,10,11,12,13,14,15,16] It is intuitively clear why the identification of the most influential nodes in a network, those that have a key role in leading and routing information, is of fundamental importance. Consider a general dynamical system based on N interconnected nodes These nodes pursue a final state by observing their neighbours and trying to minimise the relative differences. Such group dynamics are described through dxi dt
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