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A database of minima and transition states corresponds to a network where theminima represent nodes and the transition states correspond to edges betweenthe pairs of minima they connect via steepest-descent paths. Here we constructnetworks for small clusters bound by the Morse potential for a selection ofphysically relevant parameters, in two and three dimensions. The properties ofthese unweighted and undirected networks are analysed to examine two features:whether they are small-world, where the shortest path between nodes involvesonly a small number or edges; and whether they are scale-free, having a degreedistribution that follows a power law. Small-world character is present, butstatistical tests show that a power law is not a good fit, so the networks arenot scale-free. These results for clusters are compared with the correspondingproperties for the molecular and atomic structural glass formersortho-terphenyl and binary Lennard-Jones. These glassy systems do not showsmall-world properties, suggesting that such behaviour is linked to thestructure-seeking landscapes of the Morse clusters.

Properties of Kinetic Transition Networks for Atomic Clusters and Glassy Solids