  The configuration space network (CSN) of a dynamical system is an effective
approach to represent the ensemble of configurations sampled during a
simulation and their dynamic connectivity. To elucidate the connection between
the CSN topology and the underlying free-energy landscape governing the system
dynamics and thermodynamics, an analytical soluti on is provided to explain the
heavy tail of the degree distribution, neighbor co nnectivity and clustering
coefficient. This derivation allows to understand the universal CSN network
topology observed in systems ranging from a simple quadratic well to the native
state of the beta3s peptide and a 2D lattice heteropolymer. Moreover CSN are
shown to fall in the general class of complex networks describe d by the
fitness model.
