  We study the synchronized interval in undirected and unweighted random
networks of coupled oscillators as a function of the number of edges. In many
coupled oscillator systems, synchronization is stable in a finite interval of
coupling parameter, which we define as the synchronized interval. We find in
random networks, the width of the synchronized interval is maximum for an
optimal number of edges. We derive analytically an estimation for this optimal
value of the number of edges. In small networks, the analytical estimation
deviates from the numerical results. However, in large networks the analytical
and numerical results are in excellent agreement.
