  The complex network framework has been successfully applied to the analysis
of climatological data, providing, for example, a better understanding of the
mechanisms underlying reduced predictability during El Ni\~no or La Ni\~na
years. Despite the large interest that climate networks have attracted, several
issues remain to be investigated. Here we focus in the influence of the
periodic solar forcing in climate networks constructed via similarities of
monthly averaged surface air temperature (SAT) anomalies. We shift the time
series in each pair of nodes such as to superpose their seasonal cycles. In
this way, when two nodes are located in different hemispheres we are able to
quantify the similarity of SAT anomalies during the winters and during the
summers. We find that data time-shifting does not significantly modify the
network area weighted connectivity (AWC), which is the fraction of the total
area of the Earth to which each node is con- nected. This unexpected network
property can be understood in terms of how data time-shifting modifies the
strength of the links connecting geographical regions in different hemispheres,
and how these modifications are washed out by averaging the AWC.
