  The influence of networks topology on collective properties of dynamical
systems defined upon it is studied in the thermodynamic limit. A network model
construction scheme is proposed where the number of links, the average
eccentricity and the clustering coefficient are controlled. This is done by
rewiring links of a regular one dimensional chain according to a probability
$p$ within a specific range $r$, that can depend on the number of vertices $N$.
We compute the thermodynamic behavior of a system defined on the network, the
$XY-$rotors model, and monitor how it is affected by the topological changes.
We identify the network dimension $d$ as a crucial parameter: topologies with
$d\textless{}2$ exhibit no phase transitions while ones with $d\textgreater{}2$
display a second order phase transition. Topologies with $d=2$ exhibit states
characterized by infinite susceptibility and macroscopic chaotic/turbulent
dynamical behavior. These features are also captured by $d$ in the finite size
context.
