Symmetry and asymmetry depends on the distribution of the initial connectivity.

<p><b>A</b> Example of an adjacency matrix in a random network with pruning parameter and symmetry measure According with the <i>p</i>-value test with the null hypothesis of random connectivity and with a level of confidence of the symmetry of this network is significant if the distribution of the initial connections is uniform but is non-significant if the initial distribution of the connections is Gaussian. Therefore, in the first case it should be regarded as a non-random network whereas in the second case as a random network. <b>B</b> The same as A but with pruning parameter and symmetry measure In this case, with the same hypothesis test, the situation is reversed: the network should be considered random for initial uniform distribution of connections, but non-random for initial Gaussian-distributed connections (see the discussion in the text).