For network scientists, it has always been an interesting problem to identify the influential nodes in a given network. The k-shell decomposition method is a widely used method which assigns a shell-index value to each node based on its influential power. The k-shell method requires the global information of the network to compute the shell-index of a node that is infeasible for large-scale real-world dynamic networks. In this work, we propose a method to estimate the shell-index of a node using its local information. We also propose hill-climbing based approach to hit the top-ranked nodes in a small number of steps. We further discuss a method to estimate the rank of a node based on the proposed estimator.
Core-periphery structure has been studied in the wide variety of networks, such as financial network @cite_38 @cite_14 , human-brain network @cite_45 @cite_23 , nervous system of C. elegans worm @cite_27 , blog networks @cite_34 , scientific publication network @cite_48 , collaboration network @cite_35 @cite_59 , protein interaction networks @cite_5 , communication network of software development team @cite_71 @cite_52 @cite_50 @cite_24 , hollywood collaboration network @cite_61 , language network @cite_53 , YouTube social interaction network @cite_20 , metabolic networks @cite_68 , etc. proposed a method to generate all graphs for a given shell-index sequence @cite_4 .
@cite_35 @cite_71 @cite_5 @cite_20 @cite_38 @cite_4 @cite_48 @cite_52 @cite_23 @cite_68 @cite_27 @cite_50 @cite_34 @cite_61 @cite_14 @cite_53 @cite_24 @cite_45 @cite_59
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The network of international co-authorship relations has been dominated by certain European nations and the USA, but this network is rapidly expanding at the global level. Between 40 and 50 countries appear in the center of the international network in 2011, and almost all (201) nations are nowadays involved in international collaboration. In this brief communication, we present both a global map with the functionality of a Google Map (zooming, etc.) and network maps based on normalized relations. These maps reveal complementary aspects of the network. International collaboration in the generation of knowledge claims (that is, the context of discovery) changes the structural layering of the sciences. Previously, validation was at the global level and discovery more dependent on local contexts. This changing relationship between the geographical and intellectual dimensions of the sciences also has implications for national science policies. The concept of the core group of developers is important and often discussed in empirical studies of FLOSS projects. This paper examines the question, "how does one empirically distinguish the core?" Being able to identify the core members of a FLOSS development project is important because many of the processes necessary for successful projects likely involve core members differently than peripheral members, so analyses that mix the two groups will likely yield invalid results. We compare 3 analysis approaches to identify the core: the named list of developers, a Bradfords law analysis that takes as the core the most frequent contributors and a social network analysis of the interaction pattern that identifies the core in a core-and-periphery structure. We apply these measures to the interactions around bug fixing for 116 SourceForge projects. The 3 techniques identify different individuals as core members; examination of which individuals are identified leads to suggestions for refining the measures. All 3 measures though suggest that the core of FLOSS projects is a small fraction of the total number of contributors. Background Characterizing the structural properties of protein interaction networks will help illuminate the organizational and functional relationships among elements in biological systems. In this paper, we present results of an empirical investigation into the social structure of YouTube, addressing friend relations and their correlation with tags applied to uploaded videos. Results indicate that YouTube producers are strongly linked to others producing similar content. Furthermore, there is a socially cohesive core of producers of mixed content, with smaller cohesive groups around Korean music video and anime music videos. Thus, social interaction on YouTube appears to be structured in ways similar to other social networking sites, but with greater semantic coherence around content. These results are explained in terms of the relationship of video producers to the tagging of uploaded content on the site. We explore the network topology arising from a dataset of the overnight interbank transactions on the e-MID trading platform from January 1999 to December 2010. In order to shed light on the hierarchical structure of the banking system, we estimate different versions of a core---periphery model. Our main findings are: (1) the identified core is quite stable over time in its size as well as in many structural properties, (2) there is also high persistence over time of banks' identified positions as members of the core or periphery, (3) allowing for asymmetric coreness' with respect to lending and borrowing considerably improves the fit and reveals a high level of asymmetry and relatively little correlation between banks' in-coreness' and out-coreness', and (4) we show that the identified core---periphery structure could not have been obtained spuriously from random networks. During the financial crisis of 2008, the reduction of interbank lending was mainly due to core banks reducing their numbers of active outgoing links. The k-core decomposition is a widely studied summary statistic that describes a graph’s global connectivity structure. In this paper, we move beyond using k-core decomposition as a tool to summarize a graph and propose using k-core decomposition as a tool to model random graphs. We propose using the shell distribution vector, a way of summarizing the decomposition, as a sufficient statistic for a family of exponential random graph models. We study the properties and behavior of the model family, implement a Markov chain Monte Carlo algorithm for simulating graphs from the model, implement a direct sampler from the set of graphs with a given shell distribution, and explore the sampling distributions of some of the commonly used complementary statistics as good candidates for heuristic model fitting. These algorithms the provide first fundamental steps necessary for solving the following problems: parameter estimation in this ERGM, extending the model to its Bayesian relative, and developing a rigorous methodology for testing goodness of fit of the model and model selection. The methods are applied to a synthetic network as well as the well-known Sampson monks dataset. In recent years there has been a growing interest in the role of networks and clusters in the global economy. Despite being a popular research topic in economics, sociology and urban studies, geographical clustering of human activity has often been studied by means of predetermined geographical units, such as administrative divisions and metropolitan areas. This approach is intrinsically time invariant and it does not allow one to differentiate between different activities. Our goal in this paper is to present a new methodology for identifying clusters, that can be applied to different empirical settings. We use a graph approach based on k-shell decomposition to analyze world biomedical research clusters based on PubMed scientific publications. We identify research institutions and locate their activities in geographical clusters. Leading areas of scientific production and their top performing research institutions are consistently identified at different geographic scales. Abstract Intellectual relationships and collaboration networks are the basis for the development of a knowledge domain. The visual representation of such “knowledge networks” contributes to the overall understanding of intellectual collaborations in a particular knowledge domain. Based on the co-authorship data from recent journal publications over a period of five years, the authors applied social network analysis to explore the network structures and identify their network properties in the hospitality research domain. The analysis revealed the core and peripheral networks where the power law distribution was observed on the pattern of publishing academic papers. The overall network was further examined by nine research streams in both “global” and “contextual” views to understand a broad variety of the collaboration patterns of hospitality researchers. Blogs are popular communication instruments in today's web and altogether, they form the so-called blogosphere. This blogosphere has repeatedly been subject to structural analyses, and one of the findings has been the discovery of the A-List phenomenon, a cohesive group of influential blogs in the center of the blogosphere, whose exact identification remained an open issue. We use four language-specific subsets of the blogosphere, for which we aggregated the blogroll-based networks. We adapt core theory to analyse and compare the cohesion in these four data-sets, and provide a new scalable method for the identification of core-periphery structures in blog networks, which can contribute to identify A-List blogs more reliably. Prior investigations of functional specialization have focused on the response profiles of particular brain regions. Given the growing emphasis on regional covariation, we propose to reframe these questions in terms of brain ‘networks' (collections of regions jointly engaged by some mental process). Despite the challenges that investigations of the language network face, a network approach may prove useful in understanding the cognitive architecture of language. We propose that a language network plausibly includes a functionally specialized ‘core' (brain regions that coactivate with each other during language processing) and a domain-general ‘periphery' (a set of brain regions that may coactivate with the language core regions at some times but with other specialized systems at other times, depending on task demands). Framing the debate around network properties such as this may prove to be a more fruitful way to advance our understanding of the neurobiology of language. How rich functionality emerges from the invariant structural architecture of the brain remains a major mystery in neuroscience. Recent applications of network theory and theoretical neuroscience to large-scale brain networks have started to dissolve this mystery. Network analyses suggest that hierarchical modular brain networks are particularly suited to facilitate local (segregated) neuronal operations and the global integration of segregated functions. Although functional networks are constrained by structural connections, context-sensitive integration during cognition tasks necessarily entails a divergence between structural and functional networks. This degenerate (many-to-one) function-structure mapping is crucial for understanding the nature of brain networks. The emergence of dynamic functional networks from static structural connections calls for a formal (computational) approach to neuronal information processing that may resolve this dialectic between structure and function.