Diffusion of Time-Varying Signals in Complex Networks: A Structure-Dynamics Investigation Focusing the Distance to the Source of Activation

摘要

The way in which different types of dynamics unfold in complex networks isintrinsically related to the propagation of activation along nodes, which isstrongly affected by the network connectivity. In this work we investigate towhich extent a time-varying signal emanating from a specific node is modifiedas it diffuses, at the equilibrium regime, along uniformly random(Erd\H{o}s-R\'enyi) and scale-free (Barab\'asi-Albert) networks. The degree ofpreservation is quantified in terms of the Pearson cross-correlation betweenthe original signal and the derivative of the signals appearing at each nodealong time. Several interesting results are reported. First, the fact thatquite distinct signals are typically obtained at different nodes in theconsidered networks implies mean-field approaches to be completely inadequate.It has also been found that the peak and lag of the similarity time-signaturesobtained for each specific node are strongly related to the respective distancebetween that node and the source node. Such a relationship tends to decreasewith the average degree of the networks. Also, in the case of the lag, a lessintense relationship is verified for scale-free networks. No relationship wasfound between the dispersion of the similarity signature and the distance tothe source.