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Liudmila Ostroumova Prokhorenkova - One of the best experts on this subject based on the ideXlab platform.
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Clustering Coefficient of a Spatial Preferential Attachment Model
Doklady Mathematics, 2018Co-Authors: Lenar Iskhakov, Liudmila Ostroumova Prokhorenkova, Maksim Mironov, Bogumił Kamiński, Paweł PrałatAbstract:The Clustering structure of a graph in a spatial preferential attachment model whose similarity to real-world networks has been shown in many aspects is considered. The behavior of the local Clustering Coefficient is studied. Namely, the asymptotic behavior of its average value over all graph vertices of a certain degree as the graph size tends to infinity is examined. This characteristic has not been previously analyzed in the SPA model, and it reflects the typical dependence of the Clustering structure near some vertex on its degree in the graph. Additionally, it is shown that, with a high probability, there is a vertex for which the value of the Clustering Coefficient differs from its average.
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Local Clustering Coefficient in Generalized Preferential Attachment Models
Internet Mathematics, 2017Co-Authors: Alexander M. Krot, Liudmila Ostroumova ProkhorenkovaAbstract:In this paper, we analyze the local Clustering Coefficient of preferential attachment models. A general approach to preferential attachment was introduced in earlier, where a wide class of models (PA-class) was defined in terms of constraints that are sufficient for the study of the degree distribution and the Clustering Coefficient. It was previously shown that the degree distribution in all models of the PA-class follows a power law. Also, the global Clustering Coefficient was analyzed and a lower bound for the average local Clustering Coefficient was obtained. We expand the results by analyzing the local Clustering Coefficient for the PA-class of models. Namely, we analyze the behavior of C(d) which is the average local Clustering for the vertices of degree d.
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General results on preferential attachment and Clustering Coefficient
Optimization Letters, 2016Co-Authors: Liudmila Ostroumova ProkhorenkovaAbstract:This is a review paper that covers some recent results on the behavior of the Clustering Coefficient in preferential attachment networks and scale-free networks in general. The paper focuses on general approaches to network science. In other words, instead of discussing different fully specified random graph models, we describe some generic results which hold for classes of models. Namely, we first discuss a generalized class of preferential attachment models which includes many classical models. It turns out that some properties can be analyzed for the whole class without specifying the model. Such properties are the degree distribution and the global and average local Clustering Coefficients. Finally, we discuss some surprising results on the behavior of the global Clustering Coefficient in scale-free networks. Here we do not assume any underlying model.
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local Clustering Coefficient in generalized preferential attachment models
Workshop on Algorithms and Models for the Web-Graph, 2015Co-Authors: Alexander M. Krot, Liudmila Ostroumova ProkhorenkovaAbstract:In this paper, we analyze the local Clustering Coefficient of preferential attachment models. A general approach to preferential attachment was introduced in [19], where a wide class of models PA-class was defined in terms of constraints that are sufficient for the study of the degree distribution and the Clustering Coefficient. It was previously shown that the degree distribution in all models of the PA-class follows a power law. Also, the global Clustering Coefficient was analyzed and a lower bound for the average local Clustering Coefficient was obtained. We expand the results of [19] by analyzing the local Clustering Coefficient for the PA-class of models. Namely, we analyze the behavior of Cd which is the average local Clustering for the vertices of degree d.
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WAW - Local Clustering Coefficient in Generalized Preferential Attachment Models
Lecture Notes in Computer Science, 2015Co-Authors: Alexander M. Krot, Liudmila Ostroumova ProkhorenkovaAbstract:In this paper, we analyze the local Clustering Coefficient of preferential attachment models. A general approach to preferential attachment was introduced in [19], where a wide class of models PA-class was defined in terms of constraints that are sufficient for the study of the degree distribution and the Clustering Coefficient. It was previously shown that the degree distribution in all models of the PA-class follows a power law. Also, the global Clustering Coefficient was analyzed and a lower bound for the average local Clustering Coefficient was obtained. We expand the results of [19] by analyzing the local Clustering Coefficient for the PA-class of models. Namely, we analyze the behavior of Cd which is the average local Clustering for the vertices of degree d.
Egor Samosvat - One of the best experts on this subject based on the ideXlab platform.
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global Clustering Coefficient in scale free networks
Workshop on Algorithms and Models for the Web-Graph, 2014Co-Authors: Liudmila Ostroumova Prokhorenkova, Egor SamosvatAbstract:In this paper, we analyze the behavior of the global Clustering Coefficient in scale free graphs. We are especially interested in the case of degree distribution with an infinite variance, since such degree distribution is usually observed in real-world networks of diverse nature.
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WAW - Global Clustering Coefficient in Scale-Free Networks
Lecture Notes in Computer Science, 2014Co-Authors: Liudmila Ostroumova Prokhorenkova, Egor SamosvatAbstract:In this paper, we analyze the behavior of the global Clustering Coefficient in scale free graphs. We are especially interested in the case of degree distribution with an infinite variance, since such degree distribution is usually observed in real-world networks of diverse nature.
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Global Clustering Coefficient in scale-free networks
arXiv: Probability, 2014Co-Authors: Liudmila Ostroumova Prokhorenkova, Egor SamosvatAbstract:In this paper, we analyze the behavior of the global Clustering Coefficient in scale free graphs. We are especially interested in the case of degree distribution with an infinite variance, since such degree distribution is usually observed in real-world networks of diverse nature. There are two common definitions of the Clustering Coefficient of a graph: global Clustering and average local Clustering. It is widely believed that in real networks both Clustering Coefficients tend to some positive constant as the networks grow. There are several models for which the average local Clustering Coefficient tends to a positive constant. On the other hand, there are no models of scale-free networks with an infinite variance of degree distribution and with a constant global Clustering. In this paper we prove that if the degree distribution obeys the power law with an infinite variance, then the global Clustering Coefficient tends to zero with high probability as the size of a graph grows.
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generalized preferential attachment tunable power law degree distribution and Clustering Coefficient
Workshop on Algorithms and Models for the Web-Graph, 2013Co-Authors: Egor Samosvat, Liudmila Ostroumova, Alexander RyabchenkoAbstract:We propose a common framework for analysis of a wide class of preferential attachment models, which includes LCD, Buckley–Osthus, Holme–Kim and many others. The class is defined in terms of constraints that are sufficient for the study of the degree distribution and the Clustering Coefficient. We also consider a particular parameterized model from the class and illustrate the power of our approach as follows. Applying our general results to this model, we show that both the parameter of the power-law degree distribution and the Clustering Coefficient can be controlled via variation of the model parameters. In particular, the model turns out to be able to reflect realistically these two quantitative characteristics of a real network, thus performing better than previous preferential attachment models. All our theoretical results are illustrated empirically.
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generalized preferential attachment tunable power law degree distribution and Clustering Coefficient
arXiv: Combinatorics, 2012Co-Authors: Egor Samosvat, Liudmila Ostroumova, Alexander RyabchenkoAbstract:We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models. Moreover, Clustering Coefficient of these graphs can also be controlled. We propose a concrete flexible model from our class and provide an efficient algorithm for generating graphs in this model. All our theoretical results are demonstrated in practice on examples of graphs obtained using this algorithm. Moreover, observations of generated graphs lead to future questions and hypotheses not yet justified by theory.
Michael S Vitevitch - One of the best experts on this subject based on the ideXlab platform.
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Phonological neighborhood Clustering Coefficient influences word learning
The Journal of the Acoustical Society of America, 2012Co-Authors: Rutherford Goldstein, Michael S VitevitchAbstract:Network science is one approach used to analyze complex systems, and has been applied to a complex cognitive system, namely the phonological lexicon (Vitevitch, 2008). One of the measures provided by network science, termed the Clustering Coefficient or C, influences lexical processes such as speech production (Chan & Vitevitch, 2010) and speech perception (Chan & Vitevitch, 2009). The current study presents evidence of C influencing the process of learning new words. Participants were trained and tested on nonword-nonobject pairs over three lab sessions at one week intervals. Testing occurred immediately after training and after a one week interval. Participants were tested on a picture naming task, a two-alternative-forced-choice task, and a lexical decision task. Results show an advantage for learning new words with a high Clustering Coefficient. A spreading activation account is used to explain the findings.
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the influence of the phonological neighborhood Clustering Coefficient on spoken word recognition
Journal of Experimental Psychology: Human Perception and Performance, 2009Co-Authors: Kit Ying Chan, Michael S VitevitchAbstract:Clustering Coefficient—a measure derived from the new science of networks—refers to the proportion of phonological neighbors of a target word that are also neighbors of each other. Consider the words bat, hat, and can, all of which are neighbors of the word cat; the words bat and hat are also neighbors of each other. In a perceptual identification task, words with a low Clustering Coefficient (i.e., few neighbors are neighbors of each other) were more accurately identified than words with a high Clustering Coefficient (i.e., many neighbors are neighbors of each other). In a lexical decision task, words with a low Clustering Coefficient were responded to more quickly than words with a high Clustering Coefficient. These findings suggest that the structure of the lexicon (i.e., the similarity relationships among neighbors of the target word measured by Clustering Coefficient) influences lexical access in spoken word recognition. Simulations of the TRACE and Shortlist models of spoken word recognition failed to account for the present findings. A framework for a new model of spoken word recognition is proposed.
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The Clustering Coefficient of phonological neighborhoods influences spoken word recognition
The Journal of the Acoustical Society of America, 2006Co-Authors: Michael S VitevitchAbstract:Neighborhood density refers to the number of words, or neighbors, that are phonologically related to a given word. For example, the words BAT, MAT, CUT, and CAN (among others) are considered phonological neighbors of the word CAT. In contrast, the Clustering Coefficient of the neighborhood refers to the proportion of phonological neighbors that are also neighbors of each other. Among the neighbors of CAT, the words BAT and MAT are neighbors of each other, but the words BAT and CAN are not neighbors of each other. Despite the stimulus words having the same number of neighbors overall, the results of an auditory lexical decision task showed that words with a high Clustering Coefficient (i.e., most neighbors were also neighbors of each other) were responded to more quickly than words with a low Clustering Coefficient (i.e., few neighbors were also neighbors of each other). These results suggest that some aspects of phonological similarity (i.e., Clustering Coefficient) might facilitate lexical activation, whereas other aspects of phonological similarity (i.e., neighborhood density) influence a later, decision stage of processing characterized by competition among activated word‐forms. [Work supported by NIH.]
Kit Ying Chan - One of the best experts on this subject based on the ideXlab platform.
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the influence of the phonological neighborhood Clustering Coefficient on spoken word recognition
Journal of Experimental Psychology: Human Perception and Performance, 2009Co-Authors: Kit Ying Chan, Michael S VitevitchAbstract:Clustering Coefficient—a measure derived from the new science of networks—refers to the proportion of phonological neighbors of a target word that are also neighbors of each other. Consider the words bat, hat, and can, all of which are neighbors of the word cat; the words bat and hat are also neighbors of each other. In a perceptual identification task, words with a low Clustering Coefficient (i.e., few neighbors are neighbors of each other) were more accurately identified than words with a high Clustering Coefficient (i.e., many neighbors are neighbors of each other). In a lexical decision task, words with a low Clustering Coefficient were responded to more quickly than words with a high Clustering Coefficient. These findings suggest that the structure of the lexicon (i.e., the similarity relationships among neighbors of the target word measured by Clustering Coefficient) influences lexical access in spoken word recognition. Simulations of the TRACE and Shortlist models of spoken word recognition failed to account for the present findings. A framework for a new model of spoken word recognition is proposed.
Dengfeng Sun - One of the best experts on this subject based on the ideXlab platform.
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ECC - Weighted Clustering Coefficient maximization for air transportation networks
2013 European Control Conference (ECC), 2013Co-Authors: Julien Ponton, Peng Wei, Dengfeng SunAbstract:In transportation networks the robustness of a network regarding nodes and links failures is a key factor for its design. At the same time, traveling passengers usually prefer the itinerary with fewer legs. The average Clustering Coefficient can be used to measure the robustness of a network. A high average Clustering Coefficient is often synonymous with a lower average travel distance and fewer number of legs. In this paper we present the average weighted Clustering Coefficient maximization problem, and give several solution methods based on branch and bound algorithm, dynamic programming and quadratically constrained programs.
