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