tion of P is left up to the user. Recent work has shown that P must be chosen carefully when one applies modularity maximization to correlation matrices. One possible choice is to set P = I . where I is the identity matrix (MacMahon and Garlaschelli, 2015; Bazzi et al., 2014). This definition corresponds to a null model where time series are uncorrelated with one another. Thus, community detection amounts to placing as many positive correlation coefficients within each community as possible.To normalize Q so that it is bounded between 0 and 1, we scale Q ( t ) by 1 / 2 m , where 2 m = ∑ ij | W$_{ij}$ | . It is worth noting that the modularity function used here differs from most standard approaches for dealing with signed networks. Traditionally, signed net- works are sub-divided into two separate networks: one containing just positive connections: and Modularity functions are then defined for both the positive and negative components as: Q ± = $^{∑}$$_{ij}$[ W ± ij − P ± $_{ij}$] δ ( g$_{i}$,g$_{j}$ ). The choice of how to com- bine the two components to obtain the total modularity is left up to the user, though a number of weighting schemes have been proposed (G´ omez et al., 2009; Rubinov and Sporns, 2011). In general, the total modularity is of the form: Q = c $^{+}$Q$^{+}$− c $^{−}$Q$^{−}$, where c ± are constants. Thus, modularity maximization for signed networks can be viewed as an attempt to maximize the modularity of positive connections while penalizing negative connections when they fall within 12 W − ij =      − W$_{ij}$, if W$_{ij}$ < 0 0 , otherwise W + ij =      W$_{ij}$, if W$_{ij}$ > 0 0 , otherwise