Toward a Next Generation of Network Models for the Web

It is generally thought that the World Wide Web belongs to the class of complex networks that is scale-free: the distribution of the number of links that nodes have follows a power law ('rich-get-richer' effect). This phenomenon is explained by a combination of theoretical-computational and empirical analysis based on stochastic network models. However, current network models embody a number of assumptions and idealizations that are not valid for the Web. Better and richer network models are needed, in association with a much more refined and in-depth empirical data gathering and analysis. In particular, the understanding of the dynamics leaves much to desire. In this paper we present a dynamic network model that avoids a number of unrealistic idealizations commonly introduced. We show how properties such as average degree and power laws are the outcome of dynamic network parameters. Exemplified by a Wikipedia case study, we show how these dynamic parameters might be empirically measured directly. We falsify several widely held ideas about the emergence of power laws: (i) that they are related to growing networks; (ii) that they are related to (linear) preferential attachment; (iii) that they may hold strictly. Power laws do not have the status of a first principle in networks: if they hold, they are just conditional and approximate empirical regularities.