Topological Randomness and Number of Edges Predict Modular Structure in Functional Brain Networks.

In a recent paper, Bassett et al. (2011) have analyzed the static and dynamic organization of functional brain networks in humans. We here focus on the first claim made in this paper, which states that the static modular structure of such networks is nested with respect to time. Bassett et al. (2011) argue that this graded structure underlines a “multiscale modular structure”. In this letter, however, we show that such a relationship is substantially mediated by an increase in the random variation of the correlation coefficients computed at different time scales. In page 8 of their Supplementary Information, Bassett et al. (2011) report that the size of the mean correlation diminishes with the size of the time window. Such a decrease in overall correlation will generally have two effects: (i) networks ’ topologies will become increasingly more random and (ii) the number of significant edges will decrease. In this letter, we use synthetic data sets to show that these two phenomena are likely to be associated with a higher number of modules, thereby potentially explaining the apparent multiscale modular structure described by Bassett et al. (2011). Our simulations are based on the unweighted unsigned version of the modularity algorithm of Clauset et al. (2004), but may be extrapolated to weighted signed adjacency matrices. In panel (A) of figure 1, we have generated 1,000 unweighted lattices based on 112 vertices as i