Abstract
D.Watts and S.Strogatz proposed the two characteristics, L (characteristic path length) and C (clustering coefficient), to define Small World, and they modeled Beta-Graph, which produces Small World Network. This study has triggered lots of researchers in different fields. Recently, it has been suggested that associative memory networks with Small World can provide the same performance as random networks, however these studies have not showed clearly that the networks organize Small World, because their Small World Network is produced by Beta-Graph. Beta-Graph is a simple model which has only one parameter, rewiring probability p, therefore it is difficult to discriminate whether the network constitutes Small World Network or not. To reveal appearance of Small World, it is necessity to measure the networks by using L and C. The purpose of this paper is to organize Hopfield network which constitutes Small World Network and provides the same performance as random networks at small cost, and show that the structure of Small World leads to high performance in associative memory problem by measuring L and C.
