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By dividing potential energy landscapes into basins of attractionssurrounding minima and linking those basins that are connected by transitionstate valleys, a network description of energy landscapes naturally arises.These networks are characterized in detail for a series of small Lennard-Jonesclusters and show behaviour characteristic of small-world and scale-freenetworks. However, unlike many such networks, this topology cannot reflect therules governing the dynamics of network growth, because they are static spatialnetworks. Instead, the heterogeneity in the networks stems from differences inthe potential energy of the minima, and hence the hyperareas of theirassociated basins of attraction. The low-energy minima with large basins ofattraction act as hubs in the network.Comparisons to randomized networks withthe same degree distribution reveals structuring in the networks that reflectstheir spatial embedding.Comment: 14 pages, 11 figure

Characterizing the network topology of the energy landscapes of atomic clusters