  In this work, we propose a scheme that provides an analytical estimate for
the time-dependent degree distribution of some networks. This scheme maps the
problem into a random walk in degree space, and then we choose the paths that
are responsible for the dominant contributions. The method is illustrated on
the dynamical versions of the Erd\"os-R\'enyi and Watts-Strogatz graphs, which
were introduced as static models in the original formulation. We have succeeded
in obtaining an analytical form for the dynamics Watts-Strogatz model, which is
asymptotically exact for some regimes.
