How to quantify 'small-world networks'?

Recently Watts and Strogatz emphasized the widespread relevance of 'small w orlds' and studied numerically networks between complete regularity and com plete randomness. In this letter, I derive simple analytical expressions wh ich can reproduce the empirical observations. It is shown how a few random connections can turn a regular network into a 'small-world network' with a short global connection but persisting local clustering.