From Scale-free to Erdos-Renyi Networks

We analyze a model that interpolates between scale-free and Erdos-Renyi networks. The model introduced generates a one-parameter family of networks and allows to analyze the role of structural heterogeneity. Analytical calculations are compared with extensive numerical simulations in order to describe the transition between these two important classes of networks. Finally, an application of the proposed model to the study of the percolation transition is presented.Comment: 8 pages, 6 figure

The Bak-Sneppen Model on Scale-Free Networks

We investigate by numerical simulations and analytical calculations the Bak-Sneppen model for biological evolution in scale-free networks. By using large scale numerical simulations, we study the avalanche size distribution and the activity time behavior at nodes with different connectivities. We argue the absence of a critical barrier and its associated critical behavior for infinite size systems. These findings are supported by a single site mean-field analytic treatment of the model.Comment: 5 pages and 3 eps figures. Final version appeared in Europhys. Let

Synchronizability determined by coupling strengths and topology on Complex Networks

We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we unveiled how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks. Here, we provide more evidence on this phenomenon extending the previous work to networks that interpolate between homogeneous and heterogeneous topologies. We also present new details on the path towards synchronization for the evolution of clustering in the synchronized patterns. Finally, we investigate the synchronization of networks with modular structure and conclude that, in these cases, local synchronization is first attained at the most internal level of organization of modules, progressively evolving to the outer levels as the coupling constant is increased. The present work introduces new parameters that are proved to be useful for the characterization of synchronization phenomena in complex networks.Comment: 11 pages, 10 figures and 1 table. APS forma

Modified Renormalization Strategy for Sandpile Models

Following the Renormalization Group scheme recently developed by Pietronero {\it et al}, we introduce a simplifying strategy for the renormalization of the relaxation dynamics of sandpile models. In our scheme, five sub-cells at a generic scale $b$ form the renormalized cell at the next larger scale. Now the fixed point has a unique nonzero dynamical component that allows for a great simplification in the computation of the critical exponent $z$. The values obtained are in good agreement with both numerical and theoretical results previously reported.Comment: APS style, 9 pages and 3 figures. To be published in Phys. Rev.

Improved routing strategies for Internet traffic delivery

We analyze different strategies aimed at optimizing routing policies in the Internet. We first show that for a simple deterministic algorithm the local properties of the network deeply influence the time needed for packet delivery between two arbitrarily chosen nodes. We next rely on a real Internet map at the autonomous system level and introduce a score function that allows us to examine different routing protocols and their efficiency in traffic handling and packet delivery. Our results suggest that actual mechanisms are not the most efficient and that they can be integrated in a more general, though not too complex, scheme.Comment: Final versio