Rich-club Phenomenon Research Articles

Co-Occurrence Network of High-Frequency Words in the Bioinformatics Literature: Structural Characteristics and Evolution

The subjects of literature are the direct expression of the author’s research results. Mining valuable knowledge helps to save time for the readers to understand the content and direction of the literature quickly. Therefore, the co-occurrence network of high-frequency words in the bioinformatics literature and its structural characteristics and evolution were analysed in this paper. First, 242,891 articles from 47 top bioinformatics periodicals were chosen as the object of the study. Second, the co-occurrence relationship among high-frequency words of these articles was analysed by word segmentation and high-frequency word selection. Then, a co-occurrence network of high-frequency words in bioinformatics literature was built. Finally, the conclusions were drawn by analysing its structural characteristics and evolution. The results showed that the co-occurrence network of high-frequency words in the bioinformatics literature was a small-world network with scale-free distribution, rich-club phenomenon and disassortative matching characteristics. At the same time, the high-frequency words used by authors changed little in 2–3 years but varied greatly in four years because of the influence of the state-of-the-art technology.

The rich-club phenomenon of China's population flow network during the country's spring festival

This paper provides a structural analysis of the rich-club phenomenon of China's population flow network (PFN) during the country's 2015 Spring Festival. We define the PFN as the weighted network where nodes are cities and links account for the population flows. The global weighted rich-club coefficient, local weighted rich-club coefficient, assortativity and community detection are used to quantitatively characterize the rich-club tendency of the PFN. Results of global rich-club coefficient uncover the existence of a significant rich-club phenomenon in the PFN. Six cities including Beijing, Shanghai, Suzhou, Guangzhou, Shenzhen and Dongguan are identified as rich-club members. And, the value of assortativity (−0.216) shows that the network is a dissortative network. We therefore conclude that the network has typical oligarchy characteristics. Subsequently, our local rich-club coefficient analysis reveals that most (77.66%) of the nodes in the network prefer to connect to rich nodes rather than non-rich nodes. Community detection demonstrates that the network presents obvious geographical agglomeration characteristics and rich-club cities also play a dominant local role in their own “responsible” communities. These findings suggest that China's PFN during the country's Spring Festival is a specific kind of hub-and-spoke network where the rich-club cities are hubs and their interconnections form the backbones. We also identify some specific problems (e.g., the community in southwest China lacks its own rich-club cities resulting in its less integration into the national transportation and migration network). Being the first to discuss rich-club issues of population flow networks in China, findings of this research may be useful for a wide spectrum of applications ranging from population migration, urbanization and traffic infrastructure planning in China.

Optimal topologies for maximizing network transmission capacity

It has been widely demonstrated that the structure of a network is a major factor that affects its traffic dynamics. In this work, we try to identify the optimal topologies for maximizing the network transmission capacity, as well as to build a clear relationship between structural features of a network and the transmission performance in terms of traffic delivery. We propose an approach for designing optimal network topologies against traffic congestion by link rewiring and apply them on the Barabási–Albert scale-free, static scale-free and Internet Autonomous System-level networks. Furthermore, we analyze the optimized networks using complex network parameters that characterize the structure of networks, and our simulation results suggest that an optimal network for traffic transmission is more likely to have a core–periphery structure. However, assortative mixing and the rich-club phenomenon may have negative impacts on network performance. Based on the observations of the optimized networks, we propose an efficient method to improve the transmission capacity of large-scale networks.

Synaptic Plasticity and Spike Synchronisation in Neuronal Networks

Brain plasticity, also known as neuroplasticity, is a fundamental mechanism of neuronal adaptation in response to changes in the environment or due to brain injury. In this review, we show our results about the effects of synaptic plasticity on neuronal networks composed by Hodgkin-Huxley neurons. We show that the final topology of the evolved network depends crucially on the ratio between the strengths of the inhibitory and excitatory synapses. Excitation of the same order of inhibition revels an evolved network that presents the rich-club phenomenon, well known to exist in the brain. For initial networks with considerably larger inhibitory strengths, we observe the emergence of a complex evolved topology, where neurons sparsely connected to other neurons, also a typical topology of the brain. The presence of noise enhances the strength of both types of synapses, but if the initial network has synapses of both natures with similar strengths. Finally, we show how the synchronous behaviour of the evolved network will reflect its evolved topology.

Geometric explanation of the rich-club phenomenon in complex networks

The rich club organization (the presence of highly connected hub core in a network) influences many structural and functional characteristics of networks including topology, the efficiency of paths and distribution of load. Despite its major role, the literature contains only a very limited set of models capable of generating networks with realistic rich club structure. One possible reason is that the rich club organization is a divisive property among complex networks which exhibit great diversity, in contrast to other metrics (e.g. diameter, clustering or degree distribution) which seem to behave very similarly across many networks. Here we propose a simple yet powerful geometry-based growing model which can generate realistic complex networks with high rich club diversity by controlling a single geometric parameter. The growing model is validated against the Internet, protein-protein interaction, airport and power grid networks.

Empirical study on a directed and weighted bus transport network in China

Bus transport networks are directed complex networks that consist of routes, stations, and passenger flow. In this study, the concept of duplication factor is introduced to analyze the differences between uplinks and downlinks for the bus transport network of Harbin (BTN-H). Further, a new representation model for BTNs is proposed, named as directed-space P. Two empirical characteristics of BTN-H are reported in this paper. First, the cumulative distributions of weighted degree, degree, number of routes that connect to each station, and node weight (peak-hour trips at a station) uniformly follow the exponential law. Meanwhile, the node weight shows positive correlations with the corresponding weighted degree, degree, and number of routes that connect to a station. Second, a new richness parameter of a node is explored by its node weight and the connectivity, weighted connectivity, average shortest path length and efficiency between rich nodes can be fitted by composite exponential functions to demonstrate the rich-club phenomenon.

Individual variability in the anatomical distribution of nodes participating in rich club structural networks.

With recent advances in computational analyses of structural neuroimaging, it is possible to comprehensively map neural connectivity, i.e., the brain connectome. The architectural organization of the connectome is believed to play an important role in several biological processes. Central to the conformation of the connectome are connectivity hubs, which are likely to be organized in accordance with the rich club phenomenon, as evidenced by graph theory analyses of neural architecture. It is yet unclear whether rich club connectivity hubs are consistently organized in the same anatomical framework across healthy adults. We constructed the brain connectome from 43 healthy adults, based on T1-weighted and diffusion tensor MRI data. Probabilistic fiber tractography was used to evaluate connectivity between each possible pair of cortical anatomical regions of interest. Connectivity hubs were identified in accordance with the rich club phenomenon applied to binarized matrices, and the variability in frequency of hub participation was assessed node-wise across all subjects. The anatomical location of nodes participating in rich club networks was fairly consistent across subjects. The most common locations for rich club nodes were identified in integrative areas, such as the cingulate and pericingulate regions, medial aspect of the occipital areas and precuneus; or else, they were found in important and specialized brain regions (such as the oribitofrontal cortex, caudate, fusiform gyrus, and hippocampus). Marked anatomical consistency exists across healthy brains in terms of nodal participation and location of rich club networks. The consistency of connections between integrative areas and specialized brain regions highlights a fundamental connectivity pattern shared among healthy brains. We propose that approaching brain connectivity with this framework of anatomical consistencies may have clinical implications for early detection of individual variability.

Information Filtering on Coupled Social Networks

In this paper, based on the coupled social networks (CSN), we propose a hybrid algorithm to nonlinearly integrate both social and behavior information of online users. Filtering algorithm, based on the coupled social networks, considers the effects of both social similarity and personalized preference. Experimental results based on two real datasets, Epinions and Friendfeed, show that the hybrid pattern can not only provide more accurate recommendations, but also enlarge the recommendation coverage while adopting global metric. Further empirical analyses demonstrate that the mutual reinforcement and rich-club phenomenon can also be found in coupled social networks where the identical individuals occupy the core position of the online system. This work may shed some light on the in-depth understanding of the structure and function of coupled social networks.

Rich club organization supports a diverse set of functional network configurations

Brain function relies on the flexible integration of a diverse set of segregated cortical modules, with the structural connectivity of the brain being a fundamentally important factor in shaping the brain's functional dynamics. Following up on macroscopic studies showing the existence of centrally connected nodes in the mammalian brain, combined with the notion that these putative brain hubs may form a dense interconnected ‘rich club’ collective, we hypothesized that brain connectivity might involve a rich club type of architecture to promote a repertoire of different and flexibly accessible brain functions. With the rich club suggested to play an important role in global brain communication, examining the effects of a rich club organization on the functional repertoire of physical systems in general, and the brain in particular, is of keen interest. Here we elucidate these effects using a spin glass model of neural networks for simulating stable configurations of cortical activity. Using simulations, we show that the presence of a rich club increases the set of attractors and hence the diversity of the functional repertoire over and above the effects produced by scale free type topology alone. Within the networks' overall functional repertoire rich nodes are shown to be important for enabling a high level of dynamic integrations of low-degree nodes to form functional networks. This suggests that the rich club serves as an important backbone for numerous co-activation patterns among peripheral nodes of the network. In addition, applying the spin glass model to empirical anatomical data of the human brain, we show that the positive effects on the functional repertoire attributed to the rich club phenomenon can be observed for the brain as well. We conclude that a rich club organization in network architectures may be crucial for the facilitation and integration of a diverse number of segregated functions.

Observability transitions in correlated networks

Yang, Wang, and Motter [Phys. Rev. Lett. 109, 258701 (2012)] analyzed a model for network observability transitions in which a sensor placed on a node makes the node and the adjacent nodes observable. The size of the connected components comprising the observable nodes is a major concern of the model. We analyze this model in random heterogeneous networks with degree correlation. With numerical simulations and analytical arguments based on generating functions, we find that negative degree correlation makes networks more observable. This result holds true both when the sensors are placed on nodes one by one in a random order and when hubs preferentially receive the sensors. Finally, we numerically optimize networks with a fixed degree sequence with respect to the size of the largest observable component. Optimized networks have negative degree correlation induced by the resulting hub-repulsive structure; the largest hubs are rarely connected to each other, in contrast to the rich-club phenomenon of networks.

The rich club phenomenon in the classroom

We analyse the evolution of the online interactions held by college students and report on novel relationships between social structure and performance. Our results indicate that more frequent and intense social interactions generally imply better score for students engaging in them. We find that these interactions are hosted within a “rich-club”, mediated by persistent interactions among high performing students, which is created during the first weeks of the course. Low performing students try to engage in the club after it has been initially formed, and fail to produce reciprocity in their interactions, displaying more transient interactions and higher social diversity. Furthermore, high performance students exchange information by means of complex information cascades, from which low performing students are selectively excluded. Failure to engage in the rich club eventually decreases these students' communication activity towards the end of the course.

Наукометричні дослідження мереж співавторства по базі даних «Україніка наукова»

Представлено деякі напрямки дослідження комунікаційних зв’язків співавторів у різних галузях науки в Україні на базі застосування методології складних мереж. Запропоновано використання засобів оцінки монопольного становища в окремих галузях наук, досліджено феномен «клубу багатих» для мереж співавторства. На основі даних реферативної бази даних «Україніка наукова» досліджено мережі співавторства з математики, фізики, економіки, права, мовознавства. Показано, що для мереж, які досліджуються, спостерігається феномен «клубу багатих», а для вузлів цих мереж виконується закономірність Парето-Лоткі.

Local-Global Interaction and the Emergence of Scale-Free Networks with Community Structures

Understanding complex networks in the real world is a nontrivial task. In the study of community structures we normally encounter several examples of these networks, which makes any statistical inferencing a challenging endeavor. Researchers resort to computer-generated networks that resemble networks encountered in the real world as a means to generate many networks with different sizes, while maintaining the real-world characteristics of interest. The generation of networks that resemble the real world turns out in itself to be a complex search problem. We present a new rewiring algorithm for the generation of networks with unique characteristics that combine the scale-free effects and community structures encountered in the real world. The algorithm is inspired by social interactions in the real world, whereby people tend to connect locally while occasionally they connect globally. This local-global coupling turns out to be a powerful characteristics that is required for our proposed rewiring algorithm to generate networks with community structures, power law distributions both in degree and in community size, positive assortative mixing by degree, and the rich-club phenomenon.

Rich-club phenomenon based search immunization

In order to eliminate the disease with few immunized nodes and high speed,a great many immunization strategies have been proposed.Acquaintance immunization strategy is the most effective of local strategies.Based on the BA scale-free network's rich-club phenomenon and breadth first search,the paper proposed search immunization strategy based on the rich-club phenomenon which requires only local degree information.There are two types of immunization strategies,which depend on searching the neighbors' degree differently,and can also be used with different cost required.RPBSI algorithm can lead to the eradication of the epidemic by immunizing a smaller fraction of the nodes than the acquaintance immunization in BA scale-free network and scientific collaboration networks.

Insight to the express transport network

The express delivery industry is developing rapidly in recent years and has attracted attention in many fields. Express shipment service requires that parcels be delivered in a limited time with a low operation cost, which requests a high level and efficient express transport network (ETN). The ETN is constructed based on the public transport networks, especially the airline network. It is similar to the airline network in some aspects, while it has its own feature. With the complex network theory, the topological properties of the ETN are analyzed deeply. We find that the ETN has the small-world property, with disassortative mixing behavior and rich club phenomenon. It also shows difference from the airline network in some features, such as edge density and average shortest path. Analysis on the corresponding distance-weighted network shows that the distance distribution displays a truncated power-law behavior. At last, an evolving model, which takes both geographical constraint and preference attachment into account, is proposed. The model shows similar properties with the empirical results.

Empirical analysis of the worldwide maritime transportation network

In this paper we present an empirical study of the worldwide maritime transportation network (WMN) in which the nodes are ports and links are container liners connecting the ports. Using the different representations of network topology — the spaces L and P , we study the statistical properties of WMN including degree distribution, degree correlations, weight distribution, strength distribution, average shortest path length, line length distribution and centrality measures. We find that WMN is a small-world network with power law behavior. Important nodes are identified based on different centrality measures. Through analyzing weighted clustering coefficient and weighted average nearest neighbors degree, we reveal the hierarchy structure and rich-club phenomenon in the network.

Rich-club vs rich-multipolarization phenomena in weighted networks

Large-scale hierarchies characterize complex networks in different domains. Elements at the top, usually the most central or influential, may show multipolarization or tend to club together, forming tightly interconnected communities. The rich-club phenomenon quantified this tendency based on unweighted network representations. Here, we define this metric for weighted networks and discuss the appropriate normalization which preserves the nodes' strengths and discounts structural strength-strength correlations if present. We find that in some real networks the results given by the weighted rich-club coefficient can be in sharp contrast to the ones in the unweighted approach. We also discuss the ability of the scanning of weighted subgraphs formed by the high-strength hubs to unveil features in contrast to the average: the formation of local alliances in multipolarized environments, or a lack of cohesion even in the presence of rich-club ordering. Beyond structure, this analysis matters for correct understanding of functionalities and dynamical processes relying on hub interconnectedness.

Exploring the structure of the U.S. intercity passenger air transportation network: a weighted complex network approach

The U.S. airline network is one of the most advanced transportation infrastructures in the world. It is a complex geospatial structure that sustains a variety of dynamics including commercial, public, and military operations and services. We study the U.S. domestic intercity passenger air transportation network using a weighted complex network methodology, in which vertices represent cities and edges represent intercity airline connections weighted by average daily passenger traffic, non-stop distance, and average one-way fares. We find that U.S. intercity passenger air transportation network is a small-world network accompanied by dissortative mixing patterns and rich-club phenomenon, implying that large degree cities (or hub cities) tend to form high traffic volume interconnections among each other and large degree cities tend to link to a large number of small degree cities. The interhub air connections tend to form interconnected triplets with high traffic volumes, long non-stop distances, and low average one-way fares. The structure of the U.S. airline network reflects the dynamic integration of pre-existing urban and national transportation infrastructure with the competitive business strategies of commercial airlines. In this paper we apply an emerging methodology to representing, analyzing, and modeling the complex interactions associated with the physical and human elements of the important U.S. national air transport and services infrastructure.

Statistical significance of the rich-club phenomenon in complex networks

We propose that the rich-club phenomenon in complex networks should be defined in the spirit of bootstrapping, in which a null model is adopted to assess the statistical significance of the rich-club detected. Our method can serve as a definition of the rich-club phenomenon and is applied to analyze three real networks and three model networks. The results show significant improvement compared with previously reported results. We report a dilemma with an exceptional example, showing that there does not exist an omnipotent definition for the rich-club phenomenon.

Rich-club phenomenon across complex network hierarchies

The “rich-club phenomenon” in complex networks is characterized when nodes of higher degree are more interconnected than nodes with lower degree. The presence of this phenomenon may indicate several interesting high-level network properties, such as tolerance to hub failures. Here, the authors investigate the existence of this phenomenon across the hierarchies of several real-world networks. Their simulations reveal that the presence or absence of this phenomenon in a network does not imply its presence or absence in the network’s successive hierarchies, and that this behavior is even nonmonotonic in some cases.