1/fα-noise or 1/fα-phenomenon is widely considered as the signature of complexity. We demonstrate the existence of this phenomenon in various model networks, namely random, small-world, scale-free complex networks. Taking the eigenvalues of the adjacency matrix as a discrete time signal, the Fourier power spectrum of the fluctuations of the eigenvalues is analyzed in terms of their frequency. An approximately 1/f type power-law behavior is found in random networks, while the power spectrum of the fluctuations of small-world and scale-free networks featuring 1/fα noise with 1<α<2. We also present our analysis for the real-world interconnected electrical power grid. Our present work provides a new perspective to understand the complex network structures.