A surrogate for networks -- How scale-free is my scale-free network?

Abstract: Complex networks are now being studied in a wide range of disciplines across science and technology. In this paper we propose a method by which one can probe the properties of experimentally obtained network data. Rather than just measuring properties of a network inferred from data, we aim to ask how typical is that network? What properties of the observed network are typical of all such scale free networks, and which are peculiar? To do this we propose a series of methods that can be used to generate statistically likely complex networks which are both similar to the observed data and also consistent with an underlying null-hypothesis -- for example a particular degree distribution. There is a direct analogy between the approach we propose here and the surrogate data methods applied to nonlinear time series data.