A numerical method that uses linear graph theory is presented for both steady state, and extended period simulation in a pipe network including its hydraulic components (pumps, valves, junctions, etc.). The developed model is based on the Extended Linear Graph Theory (ELGT) technique. This technique is modified to include new network components such as flow control valves and tanks. The technique also expanded for extended period simulation (EPS). A newly modified method for the calculation of updated flows improving the convergence rate is being introduced. Both benchmarks, ad Actual networks are analyzed to check the reliability of the proposed method. The results reveal the finer performance of the proposed method.