Effects of traffic properties and degree heterogeneity in flow fluctuations on complex networks Communication networks are nowadays crucial in our lives and the study of the traffic features yields important advantages. In both network and traffic design, the understanding of the relationship between the traffic on a node and its fluctuations plays a key role. In this paper, we investigate the relationship between the mean traffic flow experienced by a node and its standard deviation via numerical simulations and real data analysis. In particular, we show the great influence that the degree heterogeneity of real communication systems has on the patterns of flow fluctuations observed across complex communication networks. To this end, we derive an analytical law connecting the standard deviation of flows and their mean values, we prove it via extensive numerical simulations and by means of a realistic internet traffic simulator software: NS-3. We also show that our results are robust under different assumptions regarding network topology, routing strategy and packets injection distributions.