  Stimulated by the growing interest in the applications of complex networks
framework on time series analysis, we devise a network model in which each of
$N$ nodes is associated with a random walk of length $L$. Connectivity between
any two nodes is established when the Pearson correlation coefficient(PCC) of
the corresponding time series is greater than or equal to a threshold $H$,
resulting in similarity networks with interesting properties. In particular,
these networks can have high average clustering coefficients, "small world"
property, and their degree distribution can vary from scale-free to
quasi-constant depending on $H$. A giant component of size $N$ exists until a
critical threshold $H_c$ is crossed, at which point relatively rare walks begin
to detach from it, and remain isolated. This model can be used as a first step
for building a null hypothesis for networks constructed from time series.
