In the study of the spectra of power law graphs, there are basically two competing approaches. One is to prove analogues of Wigner’s semi-circle law while the other predicts that the eigenvalues follow a power law distributions. Although the semi-circle law and the power law have nothing in common, we will show that both approaches are essentially correct if one considers the appropriate matric...

We evaluate analytically and numerically the size of the frozen core and various scaling laws for critical Boolean networks that have a power-law in- and/or out-degree distribution. To this purpose, we generalize an efficient method that has previously been used for conventional random Boolean networks and for networks with power-law in-degree distributions. With this generalization, we can als...

Power law distributions have been repeatedly observed in a wide variety of socioeconomic, biological and technological areas, including: distributions of wealth, speciesarea relationships, populations of cities, values of companies, sizes of living organisms and, more recently, distributions of documents and visitors on the Web, etc. In the vast majority of these observations, e.g., city popula...

Many empirically studied networks have approximately so-called power-law or scale-free degree distributions. In Section 1 we formally define such distributions and explore some of their properties. We also introduce and briefly compare two methods for constructing random networks with approximately power-law degree distributions: generic scale-free networks and the preferential attachment model...