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 $p$. Simulated annealing also seems to promote uniformity (over individual nodes) in mean distance to the rest of the network. This sideeffect of the annealing process might be useful in regularizing other network attributes. • The annealing process also revealed that there exist neighborhoods of low mean internodal networks. This structure of the network space might be used in designing improved search algorithms for low mean internodal distance networks. • The relation between average nodal switching complexity and mean internodal distance was briefly explored through simulated annealing. Initial sharp decreases in mean internodal distance could be had through moderate increases in switching complexity. However, further decreases required much larger increases in average complexity. Low Mean Internodal Distance Network Topologies And Simulated Annealing C. Rose Rutgers University Piscataway, New Jersey 08855