We also plan to verify our findings in other types of empirical networks, for example, gathered from the collaborative editing system Wikipedia, where we will investigate the dynamics of the editing process.
In Table 3, we report the average degree (left langle k right rangle ), average path length (left langle l right rangle ) and global clustering coefficient C for the empirical networks and for the simulated ones using the optimal set of probabilities.
For each empirical network, we created several null models and compared the proportion of links within and across genders using a chi-square test.
Results for a randomized ensemble, comparing the number of neurons in each role against that for the empirical network, are given in Table S4.
Because experimental data yield networks whose topologies do not necessarily agree with the frequently discussed archetypical networks (e.g., lattices, small-world with a certain rewiring probability, or fully random networks), it remains tricky to estimate how graph measures are influenced by changes in N and k for the empirical network.
Huss and Holme [ 38] introduce ΔQ, which is Q for the empirical network minus the average Q of a number of random networks.
The average modularity of these randomized networks is considerably lower than that of the empirical network.
We consistently obtained the same result for all replicates: the collapsed networks includes the large majority of the metabolites of the empirical network.
On the other hand, the decrease on the cooperation level shown in case A (email-class) is somewhat larger than that of the empirical email network for the same range of temptation values.
To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful.
