Abstract
Two properties of self-avoiding walk networks, constructed by connecting the nearest-neighbour points of self-avoiding walks on the square lattice, are studied numerically. The average end-to-end linear part of such networks is investigated, and is found to be proportional to the length of the walk. Secondly, random walks on this structure are studied and the associated spectral dimension of such networks is estimated to be 1.03+or-0.03, which implies that the effect of such connections affects the spectral dimension only weakly, if at all.