We consider soliton solutions of nonlinear Schrodinger equations on metric graphs by considering solitons generated by classical (usual NLS) and nonlocal nonlinear Schrodinger (NNLS) equations. In the case of classical NLS equation, solitons are assumed to be generated by PT-symmetric complex potential, while for NNLS equations are generated by cubic self-interaction. For these latter we show integrability of the problem on graphs and present a model for soliton generation.