arXiv:cond-mat/0008357v1 [cond-mat.stat-mech] 24 Aug 2000 Harmony in the Small-World Massimo Marchiori 1,2 and Vito Latora 3 1 The World Wide Web Consortium (W3C) 2 MIT Lab for Computer Science 3 Dipartimento di Fisica Universit´a di Catania and INFN Sezione Catania May 9, 2000 The Small-World phenomenon, popularly known as six degrees of separation, has been mathematically formalized by Watts and Strogatz in a study of the topological properties of a network. Small-worlds net- works are defined in terms of two quantities: they have a high clustering coefficient C like regular lattices and a short characteristic path length L typical of random networks. Physical distances are of fundamental importance in the applications to real cases, nevertheless this basic in- gredient is missing in the original formulation. Here we introduce a new concept, the connectivity length D , that gives harmony to the whole theory. D can be evaluated on a global and on a local scale and plays in turn the role of L and 1/C. Moreover it can be computed for any metrical network and not only for the topological cases. D has a pre- cise meaning in term of information propagation and describes in an unified way both the structural and the dynamical aspects of a network: 1