Title: Properties of Kinetic Transition Networks for Atomic Clusters and Glassy Solids,
Abstract: A database of minima and transition states corresponds to a network where the
minima represent nodes and the transition states correspond to edges between
the pairs of minima they connect via steepest-descent paths. Here we construct
networks for small clusters bound by the Morse potential for a selection of
physically relevant parameters, in two and three dimensions. The properties of
these unweighted and undirected networks are analysed to examine two features:
whether they are small-world, where the shortest path between nodes involves
only a small number or edges; and whether they are scale-free, having a degree
distribution that follows a power law. Small-world character is present, but
statistical tests show that a power law is not a good fit, so the networks are
not scale-free. These results for clusters are compared with the corresponding
properties for the molecular and atomic structural glass formers
ortho-terphenyl and binary Lennard-Jones. These glassy systems do not show
small-world properties, suggesting that such behaviour is linked to the
structure-seeking landscapes of the Morse clusters.