Comparison of nonlinear with linear Barabási-Albert networks

The nonlinear Barabási-Albert network (NLBA) of Krapivsky, Redner and Leyvraz (2000) is reinvestigated and modified here. We check the distribution of k(i) versus i for strong peaks and sharp gaps, where node number i has k(i) neighbors. No gaps as seen in our earlier studies of directed networks are found now, but strong peaks occur in our modified version nonlinear Barabási-Albert networks (NLBA2) while they show up only if the nonlinearity exponent is larger than one in the traditional version (NLBA1).