A statistical model for brain networks inferred from large-scale electrophysiological signals

Network science has been extensively developed to characterize structural properties of complex systems, including brain networks inferred from neuroimaging data. As a result of the inference process, networks estimated from experimentally obtained biological data, represent one instance of a larger number of realizations with similar intrinsic topology. A modeling approach is therefore needed to support statistical inference on the bottom-up local connectivity mechanisms influencing the formation of the estimated brain networks. We adopted a statistical model based on exponential random graphs (ERGM) to reproduce brain networks, or connectomes, estimated by spectral coherence between high-density electroencephalographic (EEG) signals. We validated this approach in a dataset of 108 healthy subjects during eyes-open (EO) and eyes-closed (EC) resting-state conditions. Results showed that the tendency to form triangles and stars, reflecting clustering and node centrality, better explained the global properties of the EEG connectomes as compared to other combinations of graph metrics. Synthetic networks generated by this model configuration replicated the characteristic differences found in brain networks, with EO eliciting significantly higher segregation in the alpha frequency band (8-13 Hz) as compared to EC. Furthermore, the fitted ERGM parameter values provided complementary information showing that clustering connections are significantly more represented from EC to EO in the alpha range, but also in the beta band (14-29 Hz), which is known to play a crucial role in cortical processing of visual input and externally oriented attention. These findings support the current view of the brain functional segregation and integration in terms of modules and hubs, and provide a statistical approach to extract new information on the (re)organizational mechanisms in healthy and diseased brains.Comment: Due to the limitation "The abstract field cannot be longer than 1,920 characters", the abstract appearing here is slightly shorter than that in the PDF fil

Metrics for Graph Comparison: A Practitioner's Guide

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees in data in these fields yields insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances (also known as $\lambda$ distances) and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies and different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and empirical datasets. We put forward a multi-scale picture of graph structure, in which the effect of global and local structure upon the distance measures is considered. We make recommendations on the applicability of different distance measures to empirical graph data problem based on this multi-scale view. Finally, we introduce the Python library NetComp which implements the graph distances used in this work

A morphospace of functional configuration to assess configural breadth based on brain functional networks

The best approach to quantify human brain functional reconfigurations in response to varying cognitive demands remains an unresolved topic in network neuroscience. We propose that such functional reconfigurations may be categorized into three different types: i) Network Configural Breadth, ii) Task-to-Task transitional reconfiguration, and iii) Within-Task reconfiguration. In order to quantify these reconfigurations, we propose a mesoscopic framework focused on functional networks (FNs) or communities. To do so, we introduce a 2D network morphospace that relies on two novel mesoscopic metrics, Trapping Efficiency (TE) and Exit Entropy (EE), which capture topology and integration of information within and between a reference set of FNs. In this study, we use this framework to quantify the Network Configural Breadth across different tasks. We show that the metrics defining this morphospace can differentiate FNs, cognitive tasks and subjects. We also show that network configural breadth significantly predicts behavioral measures, such as episodic memory, verbal episodic memory, fluid intelligence and general intelligence. In essence, we put forth a framework to explore the cognitive space in a comprehensive manner, for each individual separately, and at different levels of granularity. This tool that can also quantify the FN reconfigurations that result from the brain switching between mental states.Comment: main article: 24 pages, 8 figures, 2 tables. supporting information: 11 pages, 5 figure

The specificity and robustness of long-distance connections in weighted, interareal connectomes

Brain areas' functional repertoires are shaped by their incoming and outgoing structural connections. In empirically measured networks, most connections are short, reflecting spatial and energetic constraints. Nonetheless, a small number of connections span long distances, consistent with the notion that the functionality of these connections must outweigh their cost. While the precise function of these long-distance connections is not known, the leading hypothesis is that they act to reduce the topological distance between brain areas and facilitate efficient interareal communication. However, this hypothesis implies a non-specificity of long-distance connections that we contend is unlikely. Instead, we propose that long-distance connections serve to diversify brain areas' inputs and outputs, thereby promoting complex dynamics. Through analysis of five interareal network datasets, we show that long-distance connections play only minor roles in reducing average interareal topological distance. In contrast, areas' long-distance and short-range neighbors exhibit marked differences in their connectivity profiles, suggesting that long-distance connections enhance dissimilarity between regional inputs and outputs. Next, we show that -- in isolation -- areas' long-distance connectivity profiles exhibit non-random levels of similarity, suggesting that the communication pathways formed by long connections exhibit redundancies that may serve to promote robustness. Finally, we use a linearization of Wilson-Cowan dynamics to simulate the covariance structure of neural activity and show that in the absence of long-distance connections, a common measure of functional diversity decreases. Collectively, our findings suggest that long-distance connections are necessary for supporting diverse and complex brain dynamics.Comment: 18 pages, 8 figure