Network topology of the states probed by a glassy polymer during physical aging

Trajectories of a long-chain atactic polystyrene system, obtained from long Molecular Dynamics simulations in the glassy state, are mapped onto a time series of inherent structures of the potential energy landscape. The topology of the network of states formed is analyzed by employing graph-theoretical concepts. It is found that the network of the inherent structures visited by the system in the course of physical aging has both a scale-free and a small-world character. There exist minima acting as highly connected hubs in the network and trench-like sequences of states driving the system from one hub to another. In contrast to previous studies of scale-free networks in other branches of science, where the topology results from the static connectivity of the network's entities, this network is created by adding one-by-one the inherent structures traversed by the system during its evolution in time.