How to Quantify 'Small-World Networks'?

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Abstract
Recently Watts and Strogatz emphasized the widespread relevance of 'small worlds' and studied numerically networks between complete regularity and complete randomness. In this letter, I derive simple analytical expressions which 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.