This paper presents new results on network inference from observations of steady state behaviors emerging from perturbations of complex networks dynamics. We focus on the estimation of network and flow parameters using a general regularized inference formulation, which is tackled numerically using the standard technique of alternating optimization. We argue that relying only on the steady states equations removes the requirement of precisely recording transient data, and allows to meaningfully combine data from multiple experiments. To provide theoretical benchmarks we study the relationship between topological and functional characteristics of the system and the divergence between the steady state behavior observed, to give rigorous performance benchmarks. Numerical results are presented on examples with social networks and gene regulatory networks to justify our claims.