Local versus global knowledge in the Barabási-Albert scale-free network model.

The scale-free model of Barabási and Albert (BA) gave rise to a burst of activity in the field of complex networks. In this paper, we revisit one of the main assumptions of the model, the preferential attachment (PA) rule. We study a model in which the PA rule is applied to a neighborhood of newly created nodes and thus no global knowledge of the network is assumed. We numerically show that global properties of the BA model such as the connectivity distribution and the average shortest path length are quite robust when there is some degree of local knowledge. In contrast, other properties such as the clustering coefficient and degree-degree correlations differ and approach the values measured for real-world networks.