What is Small-World Property

The World Wide Web, or simply Web, is a characteristic example of a social network (Newman, 2003; Wasserman & Faust, 1994). Other examples of social networks include the food web network, scientific collaboration networks, sexual relationships networks, metabolic networks, and air transportation networks. Socials networks are usually abstracted as graphs, comprised by vertices, edges (directed or not), and in some cases, with weights on these edges. Social network theory is concerned with properties related to connectivity (degree, structure, centrality), distances (diameter, shortest paths), “resilience” (geodesic edges or vertices, articulation vertices) of these graphs, models of network growth. Social networks have been studied long before the conception of the Web. Pioneering works for the characterization of the Web as a social network and for the study of its basic properties are due to the work of Barabasi and its colleagues (Albert, Jeong & Barabasi, 1999). Later, several studies investigated other aspects like its growth (Bianconi & Barabasi, 2001; Menczer, 2004; Pennock, Flake, Lawrence, Glover, & Giles, 2002; Watts & Strogatz, 1998), its “small-world” nature in that pages can reach other pages with only a small number of links, and its scale-free nature (Adamic & Huberman, 2000; Barabasi & Albert, 1999; Barabasi & Bonabeau, 2003) (i.e., a feature implying that it is dominated by a relatively small number of Web pages that are connected to many others; these pages are called hubs and have a seemingly unlimited number of hyperlinks). Thus, the distribution of Web page linkages follows a power law in that most nodes have just a few hyperlinks and some have a tremendous number of links In that sense, the system has no “scale” (see Figure 1).