| The introduction of time in complex networks,which is known as temporal networks,brings new challenges to our research and analysis.The topology structure of temporal networks has been studied based on static networks.However,static networks ignore the impact of time dimension on network structure,as well as the time-ordering of the occurrences of nodes,This would lead to the inaccurate analysis when studying the spreading dynamics of temporal networks.In this paper,we introduce the fundamental theory and research background of complex networks,The topology structure and spreading dynamics are also discussed in considering the aging effect of temporal networks.In the paper we first analyze the time when all nodes first appear using two empirical datasets.It is noticed that there are aging effects in the appearance of nodes.The spreading ability of each node is also investigated by employing SIR model.Results suggest that the old nodes always have stronger spreading abilities than the new ones.This phenomenon tells that,the longer a node exists,the higher probability that it will infect other nodes.We further study the relationship between the spreading ability and time windows,and find that the spreading ability increases with the size of time windows.All these results indicate that the age of each node plays an important role in temporal networks,which is not considered in the tradi-tional method for computing the spreading ability.Hence,we introduce in this paper two kinds of age for each node:life time and active time.And we define the spreading speed as the ratio of a node’s spreading ability to its age.It is found that,under this definition,not all early appeared nodes have higher spreading speed.We then discuss the topology parameters of underlying temporal networks,in-cluding the temporal degree and static degree of each node.It is noticed that the temporal degree of each node keeps uncharnged within a certain period of time.This presente that all nodes have not interacted with each other during this time.Further-more,all nodes have similar degree distributions when static degree is considered.Finally,with the null-model approach,we randomly shuffle the sequence of events and eliminate the correlations between events.This null-model can also help to destroy the aging effect of each node.We analyze the relation and difference between T/2(dividing a network into two parts by time)and C/2(dividing a network into two parts by contacts).It is found that there are few connections between nodes at the initial stage.As time increases,the connections among nodes will increase.The introduction of null-model to the temporal networks demonstrates that each node has similar spreading abilities if we do not consider the aging effect,which implies that the contacts in temporal networks are well correlated. |
