The fundamental advantages of temporal networks

TL;DR

Temporal networks, despite disrupting paths, offer significant advantages such as faster controllability, lower control energy, and more compact control trajectories compared to static networks, enhancing control flexibility.

Contribution

The paper develops an analytical framework revealing that temporal networks are more controllable and energy-efficient than static networks, a counterintuitive insight.

Findings

Temporal networks reach controllability faster than static networks.

Controlling temporal networks requires significantly less energy.

Control trajectories in temporal networks are more compact.

Abstract

Despite the traditional focus of network science on static networks, most networked systems of scientific interest are characterized by temporal links. By disrupting the paths, link temporality has been shown to frustrate many dynamical processes on networks, from information spreading to accessibility. Considering the ubiquity of temporal networks in nature, we must ask: Are there any advantages of the networks' temporality? Here we develop an analytical framework to explore the control properties of temporal networks, arriving at the counterintuitive conclusion that temporal networks, compared to their static (i.e. aggregated) counterparts, reach controllability faster, demand orders of magnitude less control energy, and the control trajectories, through which the system reaches its final states, are significantly more compact than those characterizing their static counterparts. The combination of analytical, numerical and empirical results demonstrates that temporality ensures a degree of flexibility that would be unattainable in static networks, significantly enhancing our ability to control them.