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

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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 behaviour: 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.