The Time Correlation And Dynamical Fluctuation Of Temporal Network

In recent decades, the study of complex network provides a new point of view on understanding complex systems. The traditional research about complex network is based on static network in which time is ignored. Actually, time has a significant impact on most of real networks, In this paper, we aim at revealing the time effect on the temporal network structure through different methods.At first, we study the long-range correlation for the time series of nodes and contacts in temporal network through detrended fluctuation analysis. The results show that the time series of nodes and contacts in different kinds of temporal networks have different long-range correlations, but the time series of nodes and contacts in the same temporal network have similar long-range correlation. Furthermore, periodicity has a significant impact on the long-range correlation. In order to get a relatively accurate result, we also construct several null models based on empirical data. We find that the time series of the temporal network turn out to be totally randomized after Time Randomization, which provides a reference for the previous result. However, all the other null models including Time Permutation, Contact Permutation and Contact Randomization have little influence on the time series.Then we discuss the dynamical fluctuation characteristics of nodes and contacts of temporal network using factorial moments. The factorial moments can filter out statistical fluctuation of the sequences, which facilitates the study of dynamic fluctuation of the sequences. The results show that the normalized q-th order factorial moment Fqhas a scaling property with the time window number M for the time series of contacts and nodes, which indicates the phenomena of intermittency. Further we study the correlation of FqandF2 and find that there is a scaling property between them, Fq (?) F2βq.We conclude that the fluctuations of the contacts and nodes sequences in temporal network are not pure statistical and they are dynamical fluctuations. We also analyze the relationship between βq and q and find that there is a scaling property in the nodes and contacts sequences, but the scaling exponents is far from 1.3.