Energy Scaling with Control Distance in Complex Networks

It has recently been shown that the expected energy requirements of a control action applied to a complex network scales exponentially with the number of nodes that are targeted. While the exponential scaling law provides an adequate prediction of the mean required energy, it has also been shown that the spread of energy values for a particular number of targets is large. Here, we explore more closely the effect distance between driver nodes and target nodes and the magnitude of self-regulation has on the energy of the control action. We find that the energy scaling law can be written to include information about the distance between driver nodes and target nodes to more accurately predict control energy.