In this work we consider the symmetric network equilibrium problem formulated as convex minimization problem whose variables are the path flows. In order to take into account the difficulties related to the large dimension of real network problems we adopt a column generation strategy and we employ a gradient projection method within an inexact decomposition framework. We present a general decomposition algorithm model and we derive several specific algorithms for network equilibrium problems. Global convergence results are established. Computational experiments performed on medium-large dimension problems show the validity and the effectiveness of the proposed approach.