A Complex Network Framework to Model Cognition: Unveiling Correlation Structures from Connectivity

Figure 9

For model A, defined in (3), the average correlation between variables, , is plotted as a function of the characteristic network parameter, , for 3 network topologies: Erdös-Rényi of size (a), heterogeneous network of size (b), and Newman modular of size and , where intracluster (dimmer upper) and intercluster (solid bottom) correlations are held separately (c). The distribution of each value is captured by a boxplot computed from 50 independent realizations. Six different values of account for the variability of parameter. As increases, is scaled down, being the effect much larger in heterogeneous networks. In the case of ER network, grows with increasing until metric state eventually becomes unstable, and nodes are gradually absorbed by optimal state. Larger dispersion on shifts the peak towards lower values of . Conversely, for a heterogenous network, an increase on exponent leads to more stability of metric state, although stable conditions are more fragile. Larger dispersion on shifts the peak towards much lower values of . Finally, in the case of Newman modular network, stability conditions of metric state, (21), are always true for these parameters and hence the absence of the peak. For a better understanding of change of stability landscape, see Figure 6. The parameters of the model are set as Figure 8.

(a)

(b)

(c)