This paper examines small-signal stability of electrical networks composed dominantly of three-phase grid-following inverters. We show that the mere existence of a high-voltage power flow solution does not necessarily imply small-signal stability; this motivates us to develop a framework for stability analysis that systematically acknowledges inverter dynamics. We identify a suitable time-scale decomposition for the inverter dynamics, and using singular perturbation theory, obtain an analytic sufficient condition to verify small-signal stability. Compared to the alternative of performing an eigenvalue analysis of the full-order network dynamics, our analytic sufficient condition reduces computational complexity and yields insights on the role of network topology and constitution as well as inverter-filter and control parameters on small-signal stability. Numerical simulations for a radial network validate the approach and illustrate the efficiency of our analytic conditions for designing and monitoring grid-tied inverter networks.