Unraveling the effects of multiscale network entanglement on empirical systems

Complex systems are large collections of entities that organize themselves into non-trivial structures, represented as networks. One of their key emergent properties is robustness against random failures or targeted attacks -i.e., the networks maintain their integrity under removal of nodes or links. Here, we introduce network entanglement to study network robustness through a multiscale lens, encoded by the time required for information diffusion through the system. Our measure's foundation lies upon a recently developed statistical field theory for information dynamics within interconnected systems. We show that at the smallest temporal scales, the node-network entanglement reduces to degree, whereas at extremely large scales, it measures the direct role played by each node in keeping the network connected. At the meso-scale, entanglement plays a more important role, measuring the importance of nodes for the transport properties of the system. We use entanglement as a centrality measure capturing the role played by nodes in keeping the overall diversity of the information flow. As an application, we study the disintegration of empirical social, biological and transportation systems, showing that the nodes central for information dynamics are also responsible for keeping the network integrated. The dynamics of information within complex networks can be captured by a set of operators where the effect of detachment of a node defines the node-networks entanglement, which can be used as a multiscale centrality measure. Here, the authors show that the nodes with high entanglement centrality, which are critical for information dynamics, are also the ones responsible for keeping the network integrated.

Automated summary

Complex systems are large collections of entities that organize themselves into networks, and the study introduces network entanglement as a way to understand network robustness at different time scales. The entanglement between nodes and networks serves as a centrality measure, capturing the importance of nodes in information flow and network integration. Nodes with high entanglement centrality are critical for information dynamics and network integrity.