The Robustness Of Interdependent Weighted Networks

With the development of science and technology,the research of complex networks has become more and more important.In the actual complex system,the network does not exist independently,but multiple networks affect each other.At the same time,each node or each edge in the actual network may contain a weight of practical significance,so an interdependent weighted network can fit the actual system.In this paper,we mainly study the influence of local attack on two interdependent networks and the robustness of interdependent networks with partial nodes interaction under the same weight,and the effect of load cascading failure and interdependent cascading failure on systems under different weights.Through the application of percolation theory and numerical simulation,the effect of local attack on two fully interdependent networks is studied firstly.It can be found that the internal average of the network or the average between networks has similar effects on the whole system.When the average is larger,the giant component of the network is also larger,and the smaller the critical threshold point,the more stable the network.For the interdependent network which only partial nodes connect to each other,we can find that the network robustness increases with the increase of the proportion of interconnected nodes based on the generation function theory.At the same time,the framework model is analyzed and verified by using the actual data of the 32-years crude oil spot and futures prices,it can be found that the giant component of the single network has a scaling relationship with attack strengthS^p-p_c?,and near the critical point the interconnected network satisfiesS（r,p_c）^r1/?and(_?^{?S（）_rr,p})_r→0^|p-p_c|^-?.Expect that there is a universal relationship between the three scale indices near the critical attack strength of the network.Finally,the influence of the load cascading failure caused by the load distribution principle and the interdependent cascading failure caused by the interdependent relationship on the interdependent weighted network is analyzed.Due to the existence of two cascading failure modes,it is considered whether the order of the two failure modes has an impact on the stability of the network.By setting different failure mechanisms,the effects of interdependence between two networks,the initial load of nodes,and the capacity of nodes on the number of failed nodes are studied.It can be found that there is an optimal adjustment node initial load and capacity parameter values to make the network most stable and consume the least.For the analysis of this critical threshold,it is possible to determine the different effects of different interdependent methods on the network,and also indicate that the order of the two different cascading modes in the network does not affect.Through the analysis of these three different models,the understanding of the interdependent weighted network can be further deepened,and we can lay a solid foundation for further research on multiple interdependent network.