Effects of random noise on a simple class of growing network models

We investigate the effects of random noise on network systems. In particular, we consider a simple class of growing network models whose topological structure is determined by the preferred attachment A(k). We introduce a noise-induced attachment A(k) which includes fluctuations in the number of links of individual nodes due to a random noise. We carry out the numerical simulations to show that the topological structure of the networks is determined not only by A(k) but also by the strength of the noise. Analytic and numerical solutions are also presented to support this observation. In addition, we study the stability of networks against attacks under the noisy condition. Similarly, we introduce a noise-induced preferred deletion B-k, and show that noise is an essential feature to determine the stability of networks.