Abstract
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.
Highlights
Complex systems are large collections of entities that organize themselves into non-trivial structures, represented as networks
Information flow between components of complex systems can be mapped into the dynamics of a field on top of the network, governed by a general differential equation which, after linearization, reduces to a Schrodinger-like equation with a quasi-Hamiltonian H^
At very large scales β → ∞, entanglement centrality measures the direct role of each node in the integrity of network—i.e., how many disconnected components will appear if the node is detached
Summary
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. A key characteristic of complex systems, as large collections of interconnected entities, is their robustness against damage, whether it is genetic mutations in gene–gene interaction networks[1], extinction of species in ecosystems[2], failure of internet routers[3], or unavailability of transportation means[4] This common property might be deeply rooted in the unexpected resistance of their structures to disintegration[5,6,7,8,9]. Our results show that entanglement, despite being computationally slow, outperforms the considered existing centrality measures in breaking the networks up to their critical fraction
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