Tiago Simas^{1} and Luis M. Rocha^{1,2,3}

^{1}Cognitive Science Program, Indiana University, Bloomington IN, USA

^{2}School of Informatics, Indiana University, Bloomington IN, USA

^{3}FLAD Computational Biology Collaboratorium, Instituto Gulbenkian de Ciencia, Portugal

Citation: T. Simas and L.M. Rocha [2008]."Stochastic model for scale-free networks with cutoffs". * Phys. Rev. E*, **78**(6):066116. doi:10.1103/PhysRevE.78.066116

The full text is available from the * Phys. Rev. E*. The pre-print is also available. Due to mathematical notation and graphics, only the abstract is presented here.

*Abstract.*

**Background**: We propose and analyze a stochastic model which explains, analytically, the cutoff behavior of real scale-free networks previously modeled computationally by Amaral et al. [Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000)] and others. We present a mathematical model that can explain several existing computational scale-free network generation models. This yields a theoretical basis to understand cutoff behavior in complex networks, previously treated only with simulations using distinct models. Therefore, ours is an integrative approach that unifies the existing literature on cutoff behavior in scale-free networks. Furthermore, our mathematical model allows us to reach conclusions not hitherto possible with computational models: the ability to predict the equilibrium point of active vertices and to relate the growth of networks with the probability of aging. We also discuss how our model introduces a useful way to classify scale free behavior of complex networks.

*Keywords:*complex networks, graph theory, network theory (graphs), probability, random processes, stochastic processes.

For more information contact Luis Rocha at rocha@indiana.edu. Check the Web Design Credits, for due credit.

Last Modified: December 31, 2008