Hierarchical organization of functional connectivity in the mouse brain: a complex network approach

This paper represents a contribution to the study of the brain functional connectivity from the perspective of complex networks theory. More specifically, we apply graph theoretical analyses to provide evidence of the modular structure of the mouse brain and to shed light on its hierarchical organization. We propose a novel percolation analysis and we apply our approach to the analysis of a resting-state functional MRI data set from 41 mice. This approach reveals a robust hierarchical structure of modules persistent across different subjects. Importantly, we test this approach against a statistical benchmark (or null model) which constrains only the distributions of empirical correlations. Our results unambiguously show that the hierarchical character of the mouse brain modular structure is not trivially encoded into this lower-order constraint. Finally, we investigate the modular structure of the mouse brain by computing the Minimal Spanning Forest, a technique that identifies subnetworks characterized by the strongest internal correlations. This approach represents a faster alternative to other community detection methods and provides a means to rank modules on the basis of the strength of their internal edges.Comment: 11 pages, 9 figure

Thermodynamics of network model fitting with spectral entropies

An information theoretic approach inspired by quantum statistical mechanics was recently proposed as a means to optimize network models and to assess their likelihood against synthetic and real-world networks. Importantly, this method does not rely on specific topological features or network descriptors, but leverages entropy-based measures of network distance. Entertaining the analogy with thermodynamics, we provide a physical interpretation of model hyperparameters and propose analytical procedures for their estimate. These results enable the practical application of this novel and powerful framework to network model inference. We demonstrate this method in synthetic networks endowed with a modular structure, and in real-world brain connectivity networks.Comment: 11 pages, 3 figure

Thermodynamics of network model fitting with spectral entropies

An information theoretic approach inspired by quantum statistical mechanics was recently proposed as a means to optimize network models and to assess their likelihood against synthetic and real-world networks. Importantly, this method does not rely on specific topological features or network descriptors, but leverages entropy-based measures of network distance. Entertaining the analogy with thermodynamics, we provide a physical interpretation of model hyperparameters and propose analytical procedures for their estimate. These results enable the practical application of this novel and powerful framework to network model inference. We demonstrate this method in synthetic networks endowed with a modular structure, and in real-world brain connectivity networks.Comment: 11 pages, 3 figure

Graph analysis and modularity of brain functional connectivity networks: searching for the optimal threshold

Neuroimaging data can be represented as networks of nodes and edges that capture the topological organization of the brain connectivity. Graph theory provides a general and powerful framework to study these networks and their structure at various scales. By way of example, community detection methods have been widely applied to investigate the modular structure of many natural networks, including brain functional connectivity networks. Sparsification procedures are often applied to remove the weakest edges, which are the most affected by experimental noise, and to reduce the density of the graph, thus making it theoretically and computationally more tractable. However, weak links may also contain significant structural information, and procedures to identify the optimal tradeoff are the subject of active research. Here, we explore the use of percolation analysis, a method grounded in statistical physics, to identify the optimal sparsification threshold for community detection in brain connectivity networks. By using synthetic networks endowed with a ground-truth modular structure and realistic topological features typical of human brain functional connectivity networks, we show that percolation analysis can be applied to identify the optimal sparsification threshold that maximizes information on the networks' community structure. We validate this approach using three different community detection methods widely applied to the analysis of brain connectivity networks: Newman's modularity, InfoMap and Asymptotical Surprise. Importantly, we test the effects of noise and data variability, which are critical factors to determine the optimal threshold. This data-driven method should prove particularly useful in the analysis of the community structure of brain networks in populations characterized by different connectivity strengths, such as patients and controls.Comment: 15 pages, 7 figure