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Although we find that membership of neurons in specific modules are correlated with their physical nearness, the empirical network is sub-optimal in terms of both the above-mentioned constraints.

As an example, a Δ Q less than zero indicates that the empirical network is less modular than expected by chance.

To capture the level of interconnectedness that is not accounted for by node degree, Φ(k) of the empirical network is typically compared with the distribution obtained from a set of random graphs.

Obviously, a proper baseline model should be able to explain as many network features as possible, maximizing the likelihood that the empirical network was generated from that model.

Results for a randomized ensemble, comparing the number of neurons in each role against that for the empirical network, are given in Table S4.

We re-analyzed this further aiming for an optimal model fit by means of minimizing Akaike's information criterion (AIC) as heuristic for model selection [72]; the AIC-values were determined via the approximated log-likelihood that the empirical network was drawn from the distribution of the corresponding exponential random graph model with optimized parameters θ.

One empirical network was based on associations between dyads of lizards while they were inactive in their overnight refuges.

We found that the group distances for partners of hubs (we defined a hub with minimum degree of 50, n = 678) in the empirical network were significantly smaller than the values obtained from random networks (Kruskal-Wallis test, H = 62.69; df = 1; P < 0.0001), suggesting that partners are actually more functionally similar.

However, the topology of empirical networks is the very characteristic that ought to be determined through analysis.

Although this method is theoretically very appealing, it is difficult to apply because the baseline model of the empirical networks is usually unknown.

As discussed in Section 4.2, the modularity scores of the empirical networks are always higher than the ones coming from the randomly generated networks indicating that the detected modular structure is not an artifact of the degree sequence.