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A lower bound for the average number of hops in communication networks with circulant topologies of arbitrary degree

Bziuk W.

Systems Science

2006

Vol. 32, no 3

97-101

A fast computable analytical lower bound for the average number of hops (ANH) in circulant topologies is presented. Assuming uniform traffic, it only depends on the node degree and number of nodes and is applicable to the design of networks utilizing paths of minimum number of hops. The case where the traffic volume depends on the shortest number of hops between a pair of nodes is also considered. Numerical results show that circulants do have a great variation in their ANH and that the lower bound is almost exact or close to the minimum ANH.