The method presented in this paper for quickly identifying a network’s MIB using spectral clustering makes it possible to quickly measure integrated information in large brain networks.

A straightforward first-pass at an application for our method is to evaluate the long-held and untested assumptions that the “global efficiency” of a network reflects its capacity for information integration and that the modularity of a network underpins the segregation of information. A Following the procedure introduced by Watts and Strogatz [53], we systematically increased the global efficiency of our networks by increasing their rewiring probability p. Following Watts and Strogatz [53], we varied p on a log-scale between 0.001 and 0.1; to explore the full parameter space, we also linearly varied p between 0.1 and 1. For each value of p, we generated 50 100-node networks, and generated time-series data for each of those networks using the stochastic Rössler oscillator model. We then used our spectral clustering-based technique to measure geometric integrated information in these networks. B As expected [49], increasing p increased the global efficiency of the networks. Here, each dot corresponds to the global efficiency of one network of coupled Rössler oscillators with that particular value of p. The green line passes through the mean across networks. C Increasing p also systematically decreased the modularity Q of the networks. D A higher probability p of forming long-distance network connections, which increases global efficiency, led to higher integrated information (non-normalized). E There was a strong negative correlation between the networks’ structural modularity and how much information they integrate, in bits (Spearman’s ρ = -0.90, p −324). Note that the gap around Q = 0.65 occurs at the transition from the log variance of p to the linear variance of p (C). F There was a strong positive correlation between the networks’ global efficiency and how much information they integrate, in bits (Spearman’s ρ = 0.91, p −324). Note that the gap around E = 0.32 occurs at the transition from the log variance of p to the linear variance of p (B). These results support the hypothesis that network modularity supports the segregation of information, while global efficiency supports the integration of information.