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We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree distribution. We use two different approaches: the deterministic mean-field approximation used by Barabasi and Albert (but taking into account the nodes of the starting network), and the probability distribution of the degree of each node, which considers the stochastic process. Numerical simulations show that the accuracy of the predictions of the mean-field approximation depend on the contribution of the dispersion in the final distribution. The results in terms of the probability distribution of the degree of each node are very accurate when compared to numerical simulations. The analysis of the standard deviation of the degree distribution allows us to assess the influence of the starting core when fitting the model to real data.
Networks with a scale-free degree distribution are widely thought to promote cooperation in various games. Herein, by studying the well-known prisoners dilemma game, we demonstrate that this need not necessarily be true. For the very same degree sequ
The study of complex networks sheds light on the relation between the structure and function of complex systems. One remarkable result is the absence of an epidemic threshold in infinite-size scale-free networks, which implies that any infection will
Taking into account the fact that overload failures in real-world functional networks are usually caused by extreme values of temporally fluctuating loads that exceed the allowable range, we study the robustness of scale-free networks against cascadi
Weak ties play a significant role in the structures and the dynamics of community networks. Based on the susceptible-infected model in contact process, we study numerically how weak ties influence the predictability of epidemic dynamics. We first inv
We investigate the effect of a specific edge weighting scheme $sim (k_i k_j)^{beta}$ on distributed flow efficiency and robustness to cascading failures in scale-free networks. In particular, we analyze a simple, yet fundamental distributed flow mode