Scaling of average trapping time and average weighted shortest path on a residual multi-weighted crystal network

Abstract

This article constructs the residual network after some regions were damaged and detached from the original crystal network. This residual crystal network simulates the situation where parts of a computer system or power system failed after been attacked in real life. Furthermore, we assign multiple weight factors to the edges in the network, exhibiting mixed weight growth. By using the symmetry and self-similarity of the network structure, the analytical expression for the average trapping time and the average weighted shortest path on this network are solved, and the numerical results are given by taking the residual hexagonal crystal network as an example. By analyzing the network and studying the topological properties, we show the robustness of the network structure and find the residual network is more efficient for communication between nodes