Abstract

A database of minima and transition states is a network in which the minima represent nodes and transition states correspond to edges between the pairs of minima they directly connect. We have constructed such networks for small atomic clusters bound by the Morse potential with hundreds to thousands of minima at a variety of physically relevant ranges, in both two and three dimensions. The properties of the networks are analysed with particular reference to two features: whether the networks are small-world, that is a network in which most nodes are not directly connected, but the shortest path between pairs involves only a small number or edges; and whether the networks are scale-free, having a degree distribution that follows a power-law. The networks are shown to be small-world. However, modern statistical tests cast doubt on whether their degree distributions are scale-free. Morse clusters are compared with systems having a glassy character and the issues related to finding a representative subgraph are discussed.