Network Robustness Analysis Of Non-hub Nodes Failure Under Memory Or Non-memory Strategies With Limited Information

As a reflection of real complex systems,complex networks play an important role in the study of dynamics and structural complexity of modern and natural systems and rapidly become a hot interdisciplinary research area.Network robustness has also received increasing attention as an important research direction in the field of complex network research.Previous research on network robustness has focused on the failure of Hub nodes(maximum degree nodes)where the network structure information is completely known.However,due to the huge scale and dynamic change of real network,it is often impossible to access the full range of information about the network structure instantly and efficiently.Meanwhile,in real systems,Hub nodes are often well protected and difficult to damage or fail due to their importance,while Non-Hub nodes(non-maximum value nodes)are easily overlooked and therefore become the breakthrough point of choice for attackers,so the importance of Non-Hub nodes in the network cannot be ignored.In addition,when the system is attacked,this paper proposes two different attack strategies:one is that the attacked nodes can be attacked repeatedly,which is called non-memory attack;the other is that the attacked nodes cannot be attacked repeatedly,which is called memory attack.Based on the above background and the proposed two types of attack strategies,this paper proposes two types of node failure strategies,namely,Non-Hub node failure under non-memory strategy with limited information and Non-Hub node failure under memory strategy with limited information.Through Erd(?)s-Renyi(ER)random network,Scale-free(SF)network and BarabasiAlbert(BA)scale-free network investigate the effects of known nodes number information index n,average degree<k>,and the power law index λ on network robustness under two types of failure strategies,respectively.This paper proposes a theoretical framework of Non-Hub nodes failure under memory or non-memory strategies with limited information.Through theoretical analysis and numerical simulation,the influence of non-memory failure strategy for Non-Hub nodes based on limited information on ER network and scale-free network is firstly studied.When the failure node is the minimum degree node,the critical threshold 1-pc is found to increase with the average degree<k>and the information index n increases and then gradually tends to stabilise.For BA scale-free networks and SF scale-free networks,the trend between the critical threshold and the information index is similar to that of ER networks.However,for SF scale-free network,the trend between the power law index and the critical threshold is opposite,that is,the critical threshold decreases with the increase of the power law index.When the failed node is the large degree node in Non-Hub node,through numerical simulation,the paper finds that the critical threshold decreases as the information index increases and then gradually stabilizes,and the larger the degree value of the failure node,the smaller the critical threshold.These results suggest that when failing node is the minimum degree node,for ER networks,even if the average degree of the network is large enough,the network still retains strong robustness even if the attacker has enough node information.For BA scale-free network,when the attacker knows enough nodes,the more stable the network can be.For SF scale-free networks,the smaller the power law index and the more information the attacker knows about the nodes,the more robust the network becomes.When the failure node is a large degree node among Non-Hub nodes,no matter for ER network or SF scale-free network,the larger the degree of the failure node the more destructive the network system will be and the more vulnerable the network system will be to attack.Therefore,protecting nodes with larger degree value can effectively enhance the robustness of the network.Similarly,the paper studies the effect of non-memory failure strategy for Non-Hub nodes based on limited information on ER network and scale-free network,and similar conclusions were obtained.The difference between the two attack strategies is that the network system has better robustness under non-memory attack than that under memory attack.However,memory attacks can be more effective in blocking system connections,which has potential applications in real systems.Our model reveals the network robustness Non-Hub nodes failure under memory or nonmemory strategies with limited information,and provides valuable insights for designing robust practical systems.