Mesoscopics and fluctuations in networks

We describe fluctuations in finite-size networks with a complex distribution of connections, $P\left(k\right).$ We show that the spectrum of fluctuations of the number of vertices with a given degree is Poissonian. These mesoscopic fluctuations are strong in the large-degree region, where $P\left(k\right)\mathrm{}\lesssim 1/N$ $(N$ is the total number of vertices in a network), and are important in networks with fat-tailed degree distributions.