Low mean internodal distance network topologies and simulated annealing

Networks have been found through simulated annealing with mean internodal distances lower than any previously reported for a given number of nodes N with a maximum of p outgoing links per node. These networks form the closest known approximations to Moore networks. However, the improvements in mean internodal distance obtained are relatively small (a few percent) and this improvement decreases rapidly with increasing p. The relation between average nodal switching complexity and mean internodal distance is briefly explored through simulated annealing. Initial sharp decreases in mean internodal distance can be obtained through moderate increases in switching complexity. However, further decreases require much larger increases in average complexity