Global Assortativity Research Articles

Altered white matter functional pathways in Alzheimer's disease.

Alzheimer's disease (AD) is associated with functional disruption in gray matter (GM) and structural damage to white matter (WM), but the relationship to functional signal in WM is unknown. We performed the functional connectivity (FC) and graph theory analysis to investigate abnormalities of WM and GM functional networks and corpus callosum among different stages of AD from a publicly available dataset. Compared to the controls, AD group showed significantly decreased FC between the deep WM functional network (WM-FN) and the splenium of corpus callosum, between the sensorimotor/occipital WM-FN and GM visual network, but increased FC between the deep WM-FN and the GM sensorimotor network. In the clinical groups, the global assortativity, modular interaction between occipital WM-FN and visual network, nodal betweenness centrality, degree centrality, and nodal clustering coefficient in WM- and GM-FNs were reduced. However, modular interaction between deep WM-FN and sensorimotor network, and participation coefficients of deep WM-FN and splenium of corpus callosum were increased. These findings revealed the abnormal integration of functional networks in different stages of AD from a novel WM-FNs perspective. The abnormalities of WM functional pathways connect downward to the corpus callosum and upward to the GM are correlated with AD.

Local assortativity in weighted and directed complex networks

Assortativity, i.e. the tendency of a vertex to bond with another based on their similarity, such as degree, is an important network characteristic that is well-known to be relevant for the network’s robustness against attacks. Commonly it is analyzed on the global level, i.e. for the whole network. However, the local structure of assortativity is also of interest as it allows to assess which of the network’s vertices and edges are the most endangering or the most protective ones. Hence, it is quite important to analyze the contribution of individual vertices and edges to the network’s global assortativity. For unweighted networks Piraveenan et al. (2008; 2010) and Zhang et al. (2012) suggest two allegedly different approaches to measure local assortativity. In this paper we show their equivalence and propose generalized local assortativity measures that are also applicable to weighted (un)directed networks. They allow to analyze the assortative behavior of edges and vertices as well as of entire network components. We illustrate the usefulness of our measures based on theoretical and real-world weighted networks and propose new local assortativity profiles, which provide, inter alia, information about the pattern of local assortativity with respect to edge weight.

Grey matter connectome abnormalities and age-related effects in antipsychotic-naive schizophrenia.

BackgroundConvergent evidence is increasing to indicate progressive brain abnormalities in schizophrenia. Knowing the brain network features over the illness course in schizophrenia, independent of effects of antipsychotic medications, would extend our sight on this question.MethodsWe recruited 237 antipsychotic-naive patients with schizophrenia range from 16 to 73 years old, and 254 healthy controls. High-resolution T1 weighted images were obtained with a 3.0T MR scanner. Grey matter networks were constructed individually based on the similarities of regional grey matter measurements. Network metrics were compared between patient groups and healthy controls, and regression analyses with age were conducted to determine potential differential rate of age-related changes between them.FindingsNodal centrality abnormalities were observed in patients with untreated schizophrenia, particularly in the central executive, default mode and salience networks. Accelerated age-related declines and illness duration-related declines were observed in global assortativity, and in nodal metrics of left superior temporal pole in schizophrenia patients. Although no significant intergroup differences in age-related regression were observed, the pattern of network metric alternation of left thalamus indicated higher nodal properties in early course patients, which decreased in long-term ill patients.InterpretationsGlobal and nodal alterations in the grey matter connectome related to age and duration of illness in antipsychotic-naive patients, indicating potentially progressive network organizations mainly involving temporal regions and thalamus in schizophrenia independent from medication effects.FundingThe National Natural Science Foundation of China, Sichuan Science and Technology Program, the Fundamental Research Funds for the Central Universities, Post-Doctor Research Project, West China Hospital, Sichuan University , the Science and Technology Project of the Health Planning Committee of Sichuan, Postdoctoral Interdisciplinary Research Project of Sichuan University and 1.3.5 Project for Disciplines of Excellence, West China Hospital, Sichuan University.

Degree difference: a simple measure to characterize structural heterogeneity in complex networks

Despite the growing interest in characterizing the local geometry leading to the global topology of networks, our understanding of the local structure of complex networks, especially real-world networks, is still incomplete. Here, we analyze a simple, elegant yet underexplored measure, ‘degree difference’ (DD) between vertices of an edge, to understand the local network geometry. We describe the connection between DD and global assortativity of the network from both formal and conceptual perspective, and show that DD can reveal structural properties that are not obtained from other such measures in network science. Typically, edges with different DD play different structural roles and the DD distribution is an important network signature. Notably, DD is the basic unit of assortativity. We provide an explanation as to why DD can characterize structural heterogeneity in mixing patterns unlike global assortativity and local node assortativity. By analyzing synthetic and real networks, we show that DD distribution can be used to distinguish between different types of networks including those networks that cannot be easily distinguished using degree sequence and global assortativity. Moreover, we show DD to be an indicator for topological robustness of scale-free networks. Overall, DD is a local measure that is simple to define, easy to evaluate, and that reveals structural properties of networks not readily seen from other measures.

Gender homophily in online book networks

We measure the gender homophily (and other network statistics) on large-scale online book markets: amazon.com and amazon.co.uk, using datasets describing millions of books sold to readers. Large book networks are created by sales (two books are connected if many readers have bought both books) and can recommend new books to buy. The networks are analysed by the gender of their first author: is book consumption assortative by gender?Book networks are indeed gender-assortative: readers globally prefer to read from one author gender (the global assortativity coefficients by gender is around 0.4). Although 33% of first authors among all books are female, female books are not proportionally sold together with male books: an average of 20% (and median of 11%) of books co-bought with male books are female books. Instead, female books make up on average more than half of the books co-bought with other female books.The gender makeup of literary genres and structural book communities show that the gender homophily originates in a gender skew not only in certain literary genres (a fact known from prior studies), but even more strongly in certain book communities, with these book communities spanning multiple literary genres.

EDITORIAL: BEYOND SMALL-WORLD AND SCALE-FREE NETWORKS

Research on complex networks has gone through its first decade with extraordinary success. The most well-known results are probably the wide discoveries of smallworld and scale-free networks. It is indeed stimulating to observe that complex systems in different areas, including physics, sociology, telecommunications and transportation engineering, ecology, biology and even homeland security, when formulated into network models, share some nontrivial common features. These observations shed new light which helps us better understand various real-life complex systems. The papers of this Topical Section aim to help reveal in-depth details of network structures and dynamics as well as develop useful applications. The results may arguably highlight some of the current research trends. While real-life small-world and scale-free networks were being discovered or re-discovered, their global statistic properties such as assortativity and clustering coefficients have also been defined and evaluated. It is revealed that for networks with same or nearly the same nodal degrees and diameters, they may perform very differently if they are different in some of these properties. Observations on the stunning common features of different systems have been naturally followed by studies on “what make differences between them after all.” To properly reveal more details of the “differences,” research has been recently further extended, e.g., from evaluating global assortativity to detecting local community structures and from static, binary, homogeneous networks to dynamic, weighted, heterogeneous networks, etc. The results in this topical section have been presented at an International Conference on Complex Sciences: Theory and Applications (http://www.complexsys.org/) and reflect some of the research activities following this trend. The first two papers are mainly on network community structures, specifically for efficient detection of communities in homogeneous networks and extending the concept of

Some methodological issues in the study of sexual networks: from model to data to model.

Mixing between sexual activity classes is an important determinant of sexually transmitted disease transmission. However, attempts to estimate sexual mixing patterns in the field remain limited partly because of practical and methodological difficulties. To evaluate and identify appropriate sampling schemes to estimate the mixing pattern between sexual activity classes from large population networks with one or more components. The study is based on simulations of large population networks with various structural characteristics. A variety of snowball sampling schemes are applied to these networks and are evaluated by the quality of the mixing matrix estimates that they produce. Unbiased estimation of mixing patterns (global assortativity, within-group mixing of the lowest activity classes, within-group mixing of the highest activity classes) from large population networks is possible with a snowball sampling design in which the initial sample of index cases is drawn from the general population, all partners of the index case are recruited, and only one generation of partners are traced (one cycle). Simulation techniques proved useful in addressing complex methodological issues in situations where analytic results are difficult to obtain.