We consider the general networks of elastic strings with Neumann boundary feedbacks and collocated observations in this paper. By selecting an appropriate multiplier, we show that this system is input-output $L^2$-well-posed. Moreover, we verify its regularity by calculating the input-output transfer function of system. In the end, by choosing an appropriate multiplier, we give a method to construct a Lyapunov functional and prove the exponential decay of tree-shaped networks with one fixed root under velocity feedbacks acted on all leaf vertices.