We have analysed some structural properties of scale-free networks with the same degree distribution. Departing from a degree distribution obtained from the Barabási-Albert (BA) algorithm, networks were generated using four additional different algorithms (Molloy-Reed, Kalisky, and two new models named A and B) besides the BA algorithm itself. For each network, we have calculated the following structural measures: average degree of the nearest neighbours, central point dominance, clustering coefficient, the Pearson correlation coefficient, and global efficiency. We found that different networks with the same degree distribution may have distinct structural properties. In particular, model B generates decentralized networks with a larger number of components, a smaller giant component size, and a low global efficiency when compared to the other algorithms, especially compared to the centralized BA networks that have all vertices in a single component, with a medium to high global efficiency. The other three models generate networks with intermediate characteristics between B and BA models. A consequence of this finding is that the dynamics of different phenomena on these networks may differ considerably. 1. Introduction The degree distribution , defined as the fraction of vertices in the network with degree , is an important property of a complex network. In particular, the degree distribution of many real world networks [1–4] was accurately fitted by a scale-free (power-law) degree distribution where is a scaling parameter. A power-law degree distribution was observed, for instance, in networks of animal movements [5]. Such networks are examples of networks whose degree distribution may be either estimated using a questionnaire in which the number of contacting farm holdings is assessed or through the analysis of animal movement records. When there is a large number of farm holdings in the network and a data bank of animal movements is not available, we might assess the degree distribution using a questionnaire. From the estimated degree distribution, one may be interested in recovering approximately the real network to simulate, for instance, the potential spread of infectious diseases such as foot-and-mouth disease and bovine brucellosis, for which the network of animal movements is an important means of dissemination [6–8]. Nevertheless, the process of recovering a possible real network from the estimated degree distribution may lead to a misleading inference. The presence of a scale-free degree distribution does not guarantee that the recovered
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