Brain structural covariance networks in obsessive-compulsive disorder: a graph analysis from the ENIGMA Consortium.

Brain structural covariance networks reflect covariation in morphology of different brain areas and are thought to reflect common trajectories in brain development and maturation. Large-scale investigation of structural covariance networks in obsessive-compulsive disorder (OCD) may provide clues to the pathophysiology of this neurodevelopmental disorder. Using T1-weighted MRI scans acquired from 1616 individuals with OCD and 1463 healthy controls across 37 datasets participating in the ENIGMA-OCD Working Group, we calculated intra-individual brain structural covariance networks (using the bilaterally-averaged values of 33 cortical surface areas, 33 cortical thickness values, and six subcortical volumes), in which edge weights were proportional to the similarity between two brain morphological features in terms of deviation from healthy controls (i.e. z-score transformed). Global networks were characterized using measures of network segregation (clustering and modularity), network integration (global efficiency), and their balance (small-worldness), and their community membership was assessed. Hub profiling of regional networks was undertaken using measures of betweenness, closeness, and eigenvector centrality. Individually calculated network measures were integrated across the 37 datasets using a meta-analytical approach. These network measures were summated across the network density range of K = 0.10-0.25 per participant, and were integrated across the 37 datasets using a meta-analytical approach. Compared with healthy controls, at a global level, the structural covariance networks of OCD showed lower clustering (P < 0.0001), lower modularity (P < 0.0001), and lower small-worldness (P = 0.017). Detection of community membership emphasized lower network segregation in OCD compared to healthy controls. At the regional level, there were lower (rank-transformed) centrality values in OCD for volume of caudate nucleus and thalamus, and surface area of paracentral cortex, indicative of altered distribution of brain hubs. Centrality of cingulate and orbito-frontal as well as other brain areas was associated with OCD illness duration, suggesting greater involvement of these brain areas with illness chronicity. In summary, the findings of this study, the largest brain structural covariance study of OCD to date, point to a less segregated organization of structural covariance networks in OCD, and reorganization of brain hubs. The segregation findings suggest a possible signature of altered brain morphometry in OCD, while the hub findings point to OCD-related alterations in trajectories of brain development and maturation, particularly in cingulate and orbitofrontal regions

Extension of Modularity Density for Overlapping Community Structure

Modularity is widely used to effectively measure the strength of the disjoint community structure found by community detection algorithms. Although several overlapping extensions of modularity were proposed to measure the quality of overlapping community structure, there is lack of systematic comparison of different extensions. To fill this gap, we overview overlapping extensions of modularity to select the best. In addition, we extend the Modularity Density metric to enable its usage for overlapping communities. The experimental results on four real networks using overlapping extensions of modularity, overlapping modularity density, and six other community quality metrics show that the best results are obtained when the product of the belonging coefficients of two nodes is used as the belonging function. Moreover, our experiments indicate that overlapping modularity density is a better measure of the quality of overlapping community structure than other metrics considered.Comment: 8 pages in Advances in Social Networks Analysis and Mining (ASONAM), 2014 IEEE/ACM International Conference o

Clustering and Community Detection in Directed Networks: A Survey

Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed - in the sense that there is directionality on the edges, making the semantics of the edges non symmetric. An interesting feature that real networks present is the clustering or community structure property, under which the graph topology is organized into modules commonly called communities or clusters. The essence here is that nodes of the same community are highly similar while on the contrary, nodes across communities present low similarity. Revealing the underlying community structure of directed complex networks has become a crucial and interdisciplinary topic with a plethora of applications. Therefore, naturally there is a recent wealth of research production in the area of mining directed graphs - with clustering being the primary method and tool for community detection and evaluation. The goal of this paper is to offer an in-depth review of the methods presented so far for clustering directed networks along with the relevant necessary methodological background and also related applications. The survey commences by offering a concise review of the fundamental concepts and methodological base on which graph clustering algorithms capitalize on. Then we present the relevant work along two orthogonal classifications. The first one is mostly concerned with the methodological principles of the clustering algorithms, while the second one approaches the methods from the viewpoint regarding the properties of a good cluster in a directed network. Further, we present methods and metrics for evaluating graph clustering results, demonstrate interesting application domains and provide promising future research directions.Comment: 86 pages, 17 figures. Physics Reports Journal (To Appear

Network Community Detection on Metric Space

Community detection in a complex network is an important problem of much interest in recent years. In general, a community detection algorithm chooses an objective function and captures the communities of the network by optimizing the objective function, and then, one uses various heuristics to solve the optimization problem to extract the interesting communities for the user. In this article, we demonstrate the procedure to transform a graph into points of a metric space and develop the methods of community detection with the help of a metric defined for a pair of points. We have also studied and analyzed the community structure of the network therein. The results obtained with our approach are very competitive with most of the well-known algorithms in the literature, and this is justified over the large collection of datasets. On the other hand, it can be observed that time taken by our algorithm is quite less compared to other methods and justifies the theoretical findings

Different approaches to community detection

A precise definition of what constitutes a community in networks has remained elusive. Consequently, network scientists have compared community detection algorithms on benchmark networks with a particular form of community structure and classified them based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different reasons for why we would want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community detection. This problem-driven classification is useful in applied network science, where it is important to select an appropriate algorithm for the given purpose. Moreover, highlighting the different approaches to community detection also delineates the many lines of research and points out open directions and avenues for future research.Comment: 14 pages, 2 figures. Written as a chapter for forthcoming Advances in network clustering and blockmodeling, and based on an extended version of The many facets of community detection in complex networks, Appl. Netw. Sci. 2: 4 (2017) by the same author