Study On The Robustness Of Interconnected Directed Networks Under Random And Localized Attack

Many practical systems in society can be abstracted into complex networks for research.With the rapid development of science and technology,the interaction and interdependence between complex network systems is getting stronger and stronger.The failure of a node in a network may spread to other networks through the connected link,causing cascading failure of more nodes,and even causing the entire system to collapse.The robustness of the network can well measure the ability of the network to maintain its normal function when it is attacked.Therefore,the research on robustness has important practical significance,which helps to reveal the conditions and laws of actual system collapse,and proposes practical and feasible defense measures.This paper studies the robustness of interconnected directed networks under random attacks and under localized attacks.When the system is subjected to random attacks,we establish a network model that is coupled by n fully connected networks and each sub-networks coupled by connected links.Two topologies are discussed respectively: one is that each sub-network is directed random network and the inter network connection obeys Poisson distribution;the other is that each sub-network is a directed scale-free network,and the inter network connection is subject to power law distribution.We obtain the analytical solution of the Giant Strong Connected Component of each model under random attack,and verify through numerical simulation.The results show that the theory is completely consistent with the simulation.Further,for the above-mentioned network model coupled by the directed random network,the average degree allocation parameter is introduced.and the type of average degree allocation includes three types: the first is to distribute the internal and external average degree of the network while keeping the total average degree of the network unchanged.The second is to distribute the external average degree of the network while keeping the internal average degree of the network and the total external average degree.The third is to distribute the internal average degree of the network while keeping the external network average degree and the total internalaverage degree unchanged.We find that the first average degree allocation has no effect on the robustness of the network.In the second and third average degree allocation,as the average degree allocation parameter changes,the critical value of network attack strength will appear to a maximum,and the robustness of the network is the worst at the maximum point.When the system is subjected to localized attack,two different localized attack strategies are designed according to the direction of the directed link.One is to remove the root node and its neighbor nodes and the neighbor nodes of the next layer according to the out-link direction until a certain percentage is reached,and the other is to remove the root node and its neighbor nodes and the neighbor nodes of the next layer according to the in-link direction until a certain percentage is reached.For each of the two different attack methods,the robustness of a single directed ER network and two interconnected directed ER network models is discussed separately.Numerical simulations show that these two localized attack strategies have no effect on the robustness of the system.