Research On Attack And Repair Strategy Of Temporal Network

In complex network theory,networks with different attributes have different func-tions.Many research works have tried to understand how the topology and dynamics and invulnerability of complex networks change after failures or attacks.Based on the Susceptible-Infected-Refectory(SIR)epidemic spreading model,we have stud-ied different attack and repair strategies with the empirical temporal networks of co,nference and school,and used a variety of different attack and repair strategies to analyze the evolution behavior of temporal networks.The results show that the tem-poral degree is one of the best topological parameters to describe the characteristics of the temporal network.The introduction of repair cost can effectively distinguish the repair effect,of different,strategies.Firstly,we study the invulnerability under the random or targeted attacks of conference and school temporal networks.In order to understand the time effect of temporal network,the start time of the infection source is discussed under three circumstance:at the initial time to,at the arbitrary time t,or the threshold time tc.In this paper,the invulnerability refers to the structural or functional connectivity of the attacked network.The invulnerability of the network is measured according to the value f when the disconnectivity of the network is achieved.The topology of the temporal network,the relationship between spreading abilities and the fraction of at-tacked nodes f,and the relationship between temporal efficiency and f are analyzed.It is found that under different attack strategies,the temporal degree distribution-s of conference data are always heterogeneous,the static degree distributions are homogeneous;while the temporal and static degree distributions of school data are homogeneous.With the random attacks,the two networks exhibit strong invulner-ability.Under targeted attack,compared with the school network,the conference network is less invulnerability.The results show that the distribution of temporal degree can better determine the characteristics of temporal network.Secondly,based on the theory of temporal network,we propose a dynamic repair strategy and study the corresponding repair costs.The dynamic repair strategy,means that,the probability the failed node reconnects with the other nodes in the network is constantly changing.Considering the network structure,we define four repair strategies:edge proportion strategy,node priority strategy,average strategy and threshold strategy.It is found that under the edge proportion strategy,node priority strategy strategy and average strategy,the network spreading ability and temporal efficiency can be restored to about 30%of the original network respectively,and some even reached 99%.Next we study the repair cost,that is,the increase of the spreading ability of a node after adding a contact.The study shows that among the four repair strategies,the node priority strategy has a better repair effect than the average strategy and the threshold strategy,which can not only effectively improve the network spreading ability and temporal efficiency,but also effectively reduce the repair cost.Introducing repair costs enables the network to maximize network efficiency at a lower cost.Finally,a fi.xed probability repair strategy is proposed,which means,all failed nodes are reconnected with the other nodes in the network with the same probability.We analyze the network spreading abilities.The results show that under the same repair time,the larger the probability of repair,the better the network spreading abilities will achieve.As time increases,the network spreading abilities reaches the threshold state(except for r=1).The repair probability increase with the threshold time t,.When the network is attacked,the fixed probability repair strategy is of great significance in repairing the network,reducing consumption,and improving network spreading abilities.