Rich-club and page-club coefficients for directed graphs

Smilkov, Daniel; Kocarev, Ljupčo

doi:10.1016/j.physa.2010.02.001

Cited by 14 publications

(8 citation statements)

References 5 publications

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“…The World Wide Web is not really an engineered, but rather a social network-derived system. Not surprisingly, its core/periphery character is similar to that of social networks in the sense that high in-degree web-pages purposefully avoid sharing links to other high indegree web-pages (possibly decreasing the success of their competitors) [165].…”

Section: Engineered Network: the Internet The World Wide Web Transpor...mentioning

confidence: 99%

“…Importantly, several key players of the World Trade Web, such as China, France, Germany, Japan, the UK and the USA, shared on average less weight among them than anticipated from the random situation [75]. This "aversion" of key players is similar to the competitive dissociation of key members of the social elite [71][72][73][74][75]164,165] mentioned in the preceding section. Interestingly, distances of countries did not play a crucial role shaping the World Trade Web [180].…”

Section: Network Of the Economymentioning

confidence: 99%

“…Rich-club and nested network structures also showed "super-cooperation" [163]. Importantly, besides the general interconnectedness of hubs, mega-hubs ("mega-stars") of social networks often tend to avoid collaboration, and form subgroups of potential rivalry in the network core [71][72][73][164][165][166][167]. On the contrary, Twitter shows an especially high concentration of inter-connected mega-hubs, where the top 1,300 PageRank users of Twitter may impose their opinion to the whole network of more than 41 million users [168,169].…”

Section: Social Networkmentioning

confidence: 99%

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Structure and dynamics of core/periphery networks

Csermely

London

et al. 2013

Journal of Complex Networks

353

337

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Recent studies uncovered important core/periphery network structures characterizing complex sets of cooperative and competitive interactions between network nodes, be they proteins, cells, species or humans. Better characterization of the structure, dynamics and function of core/periphery networks is a key step of our understanding cellular functions, species adaptation, social and market changes. Here we summarize the current knowledge of the structure and dynamics of "traditional" core/periphery networks, rich-clubs, nested, bowtie and onion networks. Comparing core/periphery structures with network modules, we discriminate between global and local cores. The core/periphery network organization lies in the middle of several extreme properties, such as random/condensed structures, clique/star configurations, network symmetry/asymmetry, network assortativity/disassortativity, as well as network hierarchy/anti-hierarchy. These properties of high complexity together with the large degeneracy of core pathways ensuring cooperation and providing multiple options of network flow re-channelling greatly contribute to the high robustness of complex systems. Core processes enable a coordinated response to various stimuli, decrease noise, and evolve slowly. The integrative function of network cores is an important step in the development of a large variety of complex organisms and organizations. In addition to these important features and several decades of research interest, studies on core/periphery networks still have a number of unexplored areas.

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Section: Engineered Network: the Internet The World Wide Web Transpor...mentioning

confidence: 99%

Section: Network Of the Economymentioning

confidence: 99%

Section: Social Networkmentioning

confidence: 99%

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Structure and dynamics of core/periphery networks

Csermely

London

et al. 2013

Journal of Complex Networks

353

337

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“…Yet, only a few studies have analyzed the characteristics of intercity connection [38,39], such as the phenomenon of rich club of intercity linkages [40][41][42]. Researches show that urban network has a typical feature of rich club [43][44][45], that is, there is a trend of rich nodes preferentially connecting to rich nodes in the urban network. Although there has been a considerable amount of research in this area, many aspects need to be further explored.…”

Section: Review Of the Related Literaturementioning

confidence: 99%

Club Characteristic and the Proximity Effect of Travel Links between Cities in China

Chen

Zhang

2020

Complexity

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With the increasingly close relations between cities in China, it is of great significance to explore the regular characteristics of the intercity connection. Through Tencent’s population migration heat and Baidu map big data, this paper analyzes the regular characteristics of the relations between complex cities based on such index as the rich node propensity index, preference level index, and relative heat index and also investigates the influence of geographical proximity factors on the external relations of different cities. The research has the following results. Firstly, the relations between cities have obvious club characteristics. The rich nodes tend to connect with the rich nodes, while the nonrich nodes tend to connect with the nonrich nodes. Secondly, the connection between cities has the effect of hierarchical proximity, and cities mainly establish spatial connections with cities of the same level and adjacent level. Thirdly, the relations between cities also have the effect of geographical proximity, and the degree of influence of geographical proximity in low-level cities is greater than that in high-level cities. Fourthly, the external connection mode of high-level cities is to establish close contact with high-level cities adjacent to the level, with strong attraction to low-level cities adjacent to the location at the same time. The low-level cities are closely related to the high-level cities adjacent to the location and other cities of geographical proximity or adjacent level. This study helps to further understand the complex characteristics and laws of intercity connections and urban networks.

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“…Where k is the richness parameter (synaptic degree unless otherwise specified), E >k is the number of directed edges between nodes where the richness parameter is greater than k and N >k is the number of nodes which posses a richness parameter greater than k [68] [82]. However because this value tends to 28/38 monotonically increase for random networks, richness is typically measured with respect to a null model to produce a "normalized rich club coefficient", which shows how much more (or less) the given network's hub nodes connect to each other than what one would expect from chance:…”

Section: Mana Self-organizes Hubsmentioning

confidence: 99%

Cortical Circuits from Scratch: A Metaplastic Architecture for the Emergence of Lognormal Firing Rates and Realistic Topology

Tosi,

Beggs

2017

Preprint

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Our current understanding of neuroplasticity paints a picture of a complex interconnected system of dependent processes which shape cortical structure so as to produce an efficient information processing system. Indeed, the cooperation of these processes is associated with robust, stable, adaptable networks with characteristic features of activity and synaptic topology. However, combining the actions of these mechanisms in models has proven exceptionally difficult and to date no model has been able to do so without significant hand-tuning. Until such a model exists that can successfully combine these mechanisms to form a stable circuit with realistic features, our ability to study neuroplasticity in the context of (more realistic) dynamic networks and potentially reap whatever rewards these features and mechanisms imbue biological networks with is hindered. We introduce a model which combines five known plasticity mechanisms that act on the network as well as a unique metaplastic mechanism which acts on other plasticity mechanisms, to produce a neural circuit model which is both stable and capable of broadly reproducing many characteristic features of cortical networks. The MANA (metaplastic artificial neural architecture) represents the first model of its kind in that it is able to self-organize realistic, nonrandom features of cortical networks, from a null initial state (no synaptic connectivity or neuronal differentiation) with no hand-tuning of relevant variables. In the same vein as models like the SORN (self-organizing recurrent network) MANA represents further progress toward the reverse engineering of the brain at the network level.

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Rich-club and page-club coefficients for directed graphs

Cited by 14 publications

References 5 publications

Structure and dynamics of core/periphery networks

Structure and dynamics of core/periphery networks

Club Characteristic and the Proximity Effect of Travel Links between Cities in China

Cortical Circuits from Scratch: A Metaplastic Architecture for the Emergence of Lognormal Firing Rates and Realistic Topology

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