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How small is it? Comparing indices of small worldliness

  • ZACHARY P. NEAL (a1)

Abstract

Many studies have attempted to determine whether an observed network exhibits a so-called “small-world structure.” Such determinations have often relied on a conceptual definition of small worldliness proposed by Watts and Strogatz in their seminal 1998 paper, but recently several quantitative indices of network small worldliness have emerged. This paper reviews and compares three such indices—the small-world quotient (Q), a small-world metric (ω), and the small-world index(SWI)—in the canonical Watts–Strogatz re-wiring model and in four real-world networks. These analyses suggest that researchers should avoid Q, and identify considerations that should guide the choice between ω and SWI.

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