Towards a Tensor Network Representation of Complex Systems

Abstract

Complex networks are composed of nodes (entities) and edges (connections) with any arbitrary topology. There may also exist multiple types of interactions among these nodes and each node may admit different states in each of its interactions with its neighbors. Understanding complex networks dwells on understanding their structure and function. However, current representations model nodes as single-state entities that are connected to each other differently and treat their dynamics separately with some differential equations. Alternatively, a unified framework might be accessible using the tensor network representation that is already utilized in physics communities. In a sequel of chapters we introduce tensor network representation and renormalization as an alternative framework to explore the universal behaviors of complex systems. We hope that tensor networks can particularly pave the way for better understanding of the sustainable interdependent networks (Amini et al., Sustainable interdependent networks: from theory to application, 2018) through proposing efficient computational strategies and discovering insightful features of the network behaviors.