Network topology of a potential energy landscape: a static scale-free network

Here we analyze the topology of the network formed by the minima and transition states on the potential energy landscape of small clusters. We find that this network has both a small-world and scale-free character. In contrast to other scale-free networks, where the topology results from the dynamics of the network growth, the potential energy landscape is a static entity. Therefore, a fundamentally different organizing principle underlies this behavior: The potential energy landscape is highly heterogeneous with the low-energy minima having large basins of attraction and acting as the highly connected hubs in the network.