I need to analyze a correlation network where I do not know if scale-free properties are expected. Actually, I would like to know if the network has a power-law decay of the degree distribution (scale-free). Usually, a soft threshold is selected which gives such a power-law distribution, under the prior assumption that the network is scale-free. What if we cannot make that prior assumption? Are there alternative thresholding methods, so we can test for scale-free topology (or other tail distributions, like exponential) without prior bias?
The network I am working with is made of correlations between the abundances of bacteria in an ecosystem, as measured with metagenomics. The correlations are calculated from the relative abundance of each different bacteria of several soil samples. We use partial correlations to correct for confounding factors. We do not know if scale-free topology is expected.