Abstract
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.
Highlights
The degree distribution P(k), defined as the fraction of vertices in the network with degree k, is an important property of a complex network
More than one method may generate a network that shows a scale-free degree distribution, and, from these different methods, networks can emerge with different structural properties, which may impact the outcomes of the simulation of dynamical phenomena on the network
An important finding of [21] is that the simulations for the susceptible-infectedsusceptible (SIS) infectious diseases models show that the disease prevalence in Model B (MB) networks is lower than in the other networks, which may be related to the MB network structure, in which a large set of vertices are not connected to the main component of the network
Summary
The degree distribution P(k), defined as the fraction of vertices in the network with degree k, is an important property of a complex network. 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. 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-andmouth disease and bovine brucellosis, for which the network of animal movements is an important means of dissemination [6,7,8]. More than one method may generate a network that shows a scale-free degree distribution, and, from these different methods, networks can emerge with different structural properties, which may impact the outcomes of the simulation of dynamical phenomena on the network
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