Community Structure Of Brain Networks Research Articles

Weighted Stochastic Block Models of the Human Connectome across the Life Span

The human brain can be described as a complex network of anatomical connections between distinct areas, referred to as the human connectome. Fundamental characteristics of connectome organization can be revealed using the tools of network science and graph theory. Of particular interest is the network’s community structure, commonly identified by modularity maximization, where communities are conceptualized as densely intra-connected and sparsely inter-connected. Here we adopt a generative modeling approach called weighted stochastic block models (WSBM) that can describe a wider range of community structure topologies by explicitly considering patterned interactions between communities. We apply this method to the study of changes in the human connectome that occur across the life span (between 6–85 years old). We find that WSBM communities exhibit greater hemispheric symmetry and are spatially less compact than those derived from modularity maximization. We identify several network blocks that exhibit significant linear and non-linear changes across age, with the most significant changes involving subregions of prefrontal cortex. Overall, we show that the WSBM generative modeling approach can be an effective tool for describing types of community structure in brain networks that go beyond modularity.

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.

Hierarchical organization of multiscale communities in brain networks is non-tree structured

In literature of network science, a group of nodes that are densely connected within the group and are less connected with nodes outside the group is referred to as a [1]. Community structure is a fundamental property of a variety of social, biological and engineering networks. Specifically, communities in brain networks are considered to be associated with functional modules of information processing in the brain [2]. To reveal information processing architecture of the brain, therefore, it is pivotal to know individual communities and their organization in brain networks. Community structure in brain networks is characterized by hierarchical organization, which reflects that functional modules at larger scales are built up from a set of functional modules at smaller scales [3]. A number of mathematical methods for detecting communities in networks have been developed so far [1], but unfortunately few of them can consistently deal with hierarchical organization of multiscale communities. Here we propose a reliable method for detecting hierarchical organization of multiscale communities. Then we examine community structure of real brain networks by use of this method. The proposed method is based on a novel Bayesian formulation of Markov chain. The method has only one parameter, , which comes from the precision of the prior distribution of a random process. The amplitude of controls the resolution of community detection; the smaller its amplitude, the finer the size of detected communities. Quasi-static increase in causes a series of discrete phase transitions; at each transition point a subset of smaller communities (children) agglomerate a larger community (parent), thus leading to a hierarchical organization of multiscale communities. Applying this method to the neuronal network of C. elegans [4] and the macaque cortical network [5], we have found that hierarchical organization of multiscale communities in these networks is non-tree structured: Some child communities have more than one parent community (Figure ​(Figure1).1). These findings suggest efficient architecture for integration of functional modules in brain information processing: The same functional modules at lower levels can be shared by distinct functional modules at higher levels. Figure 1 Hierarchical organization of communities in the neuronal network of C. elegans. Each layer of the hierarchy is shown by horizontal alignment of red squares. Each square indicates a community detected at each layer. The size of each square indicates the ...