  We study the existence of solutions of Ricci flow equations of
Ollivier-Lin-Lu-Yau curvature defined on weighted graphs. Our work is motivated
by\cite{NLLG} in which the discrete time Ricci flow algorithm has been applied
successfully as a discrete geometric approach in detecting complex networks.
Our main result is the existence and uniqueness theorem for solutions to a
continuous time normalized Ricci flow. We also display possible solutions to
the Ricci flow on path graph and prove the Ricci flow on finite star graph with
at least three leaves converges to constant-weighted star.
