Applying the \frac{E}{2} * ln(1/\epsilon) rule, this network would require around 67,861 individual edge rewires to construct a likely sufficiently random degree-preserved graph. If we construct many random, degree preserving graphs from the real graph, we can then create a probability space for characteristics, such as reciprocity and average path length, and assess the degree to which the network could have expressed these characteristics at random. 534 networks were generated using Degree Preserving Randomization. As both reciprocity and average path length in this graph are normally distributed, and as the standard deviation for both reciprocity and average path length are far too narrow to include the observed case, we can reasonably posit that this network is expressing characteristics that are non-random (and thus open for further theory and modeling).
