I recently read the paper titled "Scale free networks are rare" (reference). This gives me heart because my very own network clusters had a degree exponent value ranging from 0.8 to 1.2 when ideal scale free networks are said to have a slope value between 2 and 3. I have two questions.
In the paper, the authors state that many biological networks are not scale free, He has also classified the networks from weakest to strongest based on their scale free nature. However, he does not make this distinction based on slope values. I fit my network with a power law line using cytoscape and it does exhibit a heavy tail. One of the criteria that the author uses to classify scale free networks is also based on the number of nodes in the tail but again, I can't find any information on how to classify a node as belonging to the tail?
The author further states that " if p ≥ 0.1, then we deem the degree sequence to be plausibly scale free, while if p < 0.1, we reject the scale-free hypothesis.
The equation being,
p(k) = C*(k^−α), let us take the example, C = 39.489, −α = -0.965 , R^2 value is 0.598 and the correlation value is 0.494. How do I calculate the value of p?