The Properties of Tree-Like Hierarchical Networks

Tree-like hierarchical structure is one of the key features in many real complex systems. To investigate its properties, a deterministic tree-like hierarchical network model is proposed. Next, the static properties of the tree-like hierarchical networks are discussed. The simulation and theoretical results prove that the artificial tree-like networks conformably possess small-world and scalefree properties well. Furthermore, the dynamic cascading failures in the tree-like hierarchical networks are investigated. A weighted tree-like cascading failure model is proposed, and the impacts of topological structure on the network robustness are investigated by a set of illustrative simulations.