We consider a network consisting of n interconnected nonlinear
subsystems. For each subsystem an ISS Lyapunov function is given
that treats the other subsystems as independent inputs. We use a
gain matrix to encode the mutual dependencies of the systems in the
network. Under a small gain assumption on the monotone operator
induced by the gain matrix, we construct a locally Lipschitz
continuous ISS Lyapunov function for the entire network by
appropriately scaling the individual Lyapunov functions for the
subsystems.