We consider a geometric entropy as a measure of complexity for Gaussian networks, namely networks having Gaussian random variables sitting on vertices and their correlations as weighted links. We then show how the network dynamics described by the well-known Ornstein–Uhlenbeck process reflects into such a measure. We unveil a crossing of the entropy time behaviors between switching on and off links. Moreover, depending on the number of links switched on or off, the entropy time behavior can be non-monotonic.