Small-world networks and the conformation space of a lattice polymer chain

We map the conformation space of a simple lattice polymer chain to a network, where (i) the vertices of the network have a one-to-one correspondence to the conformations of the chain, and (ii) a link between two vertices indicates the possibility of switching from one conformation to the other by a single Monte Carlo move of the chain. We find that the geometric properties of this network are similar to those of small-world networks, namely, the diameter of conformation space increases, for large networks, as the logarithm of the number of conformations, while locally the network appears to have low dimensionality.