Internet Mathematics最新文献_第10页

Internet Mathematics Pub Date : 2011-10-31 DOI: 10.1080/15427951.2012.625246

A. Bonato, J. Janssen, P. Prałat

引用次数: 26

Toward Quantifying Vertex Similarity in Networks 网络中顶点相似度的量化

Internet Mathematics Pub Date : 2011-10-12 DOI: 10.1080/15427951.2013.836581

Charalampos E. Tsourakakis

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引用次数: 13

Scaled Gromov Four-Point Condition for Network Graph Curvature Computation 网络图曲率计算的缩放Gromov四点条件

Internet Mathematics Pub Date : 2011-08-30 DOI: 10.1080/15427951.2011.601233

E. Jonckheere, P. Lohsoonthorn, F. Ariaei

引用次数: 23

Degree Distribution and Number of Edges between Nodes of Given Degrees in the Buckley–Osthus Model of a Random Web Graph 随机网络图的Buckley-Osthus模型中给定度节点间的度分布和边数

Internet Mathematics Pub Date : 2011-08-19 DOI: 10.1080/15427951.2011.646176

E. Grechnikov

{"title":"Degree Distribution and Number of Edges between Nodes of Given Degrees in the Buckley–Osthus Model of a Random Web Graph","authors":"E. Grechnikov","doi":"10.1080/15427951.2011.646176","DOIUrl":"https://doi.org/10.1080/15427951.2011.646176","url":null,"abstract":"Abstract In this paper, we study some important statistics of the random graph H (t) a,k in the Buckley–Osthus model, where t is the number of nodes, kt is the number of edges (so that ), and a>0 is the so-called initial attractiveness of a node. This model is a modification of the well-known Bollobás–Riordan model. First, we find a new asymptotic formula for the expectation of the number R(d, t) of nodes of a given degree d in a graph in this model. Such a formula is known for and d⩽t 1/100(a+1). Both restrictions are unsatisfactory from theoretical and practical points of view. We completely remove them. Then we calculate the covariances between any two quantities R(d 1, t) and R(d 2, t), and using the second-moment method we show that R(d, t) is tightly concentrated around its mean for all possible values of d and t. Furthermore, we study a more complicated statistic of the web graph: X(d 1, d 2, t) is the total number of edges between nodes whose degrees are equal to d 1 and d 2 respectively. We also find an asymptotic formula for the expectation of X(d 1, d 2, t) and prove a tight concentration result. Again, we do not impose any substantial restrictions on the values of d 1, d 2, and t.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"94 1","pages":"257 - 287"},"PeriodicalIF":0.0,"publicationDate":"2011-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2011.646176","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59946845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 16

Editor-in-Chief's Call for Papers 总编征稿

Internet Mathematics Pub Date : 2011-06-14 DOI: 10.1080/15427951.2011.589758

A. Bonato

引用次数: 0

Community Structures in Classical Network Models 经典网络模型中的社区结构

Internet Mathematics Pub Date : 2011-06-14 DOI: 10.1080/15427951.2011.566458

Angsheng Li, Pan Peng

引用次数: 16

Moment-Based Estimation of Stochastic Kronecker Graph Parameters 基于矩的随机Kronecker图参数估计

Internet Mathematics Pub Date : 2011-06-08 DOI: 10.1080/15427951.2012.680824

D. Gleich, A. Owen

引用次数: 39

Fast Matrix Computations for Pairwise and Columnwise Commute Times and Katz Scores 成对和列式通勤时间和Katz分数的快速矩阵计算

Internet Mathematics Pub Date : 2011-04-19 DOI: 10.1080/15427951.2012.625256

F. Bonchi, Pooya Esfandiar, D. Gleich, C. Greif, L. Lakshmanan

{"title":"Fast Matrix Computations for Pairwise and Columnwise Commute Times and Katz Scores","authors":"F. Bonchi, Pooya Esfandiar, D. Gleich, C. Greif, L. Lakshmanan","doi":"10.1080/15427951.2012.625256","DOIUrl":"https://doi.org/10.1080/15427951.2012.625256","url":null,"abstract":"Abstract We explore methods for approximating the commute time and Katz score between a pair of nodes. These methods are based on the approach of matrices, moments, and quadrature developed in the numerical linear algebra community. They rely on the Lanczos process and provide upper and lower bounds on an estimate of the pairwise scores. We also explore methods to approximate the commute times and Katz scores from a node to all other nodes in the graph. Here, our approach for the commute times is based on a variation of the conjugate gradient algorithm, and it provides an estimate of all the diagonals of the inverse of a matrix. Our technique for the Katz scores is based on exploiting an empirical localization property of the Katz matrix. We adapt algorithms used for personalized PageRank computing to these Katz scores and theoretically show that this approach is convergent. We evaluate these methods on 17 real-world graphs ranging in size from 1000 to 1,000,000 nodes. Our results show that our pairwise commute-time method and columnwise Katz algorithm both have attractive theoretical properties and empirical performance.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"8 1","pages":"112 - 73"},"PeriodicalIF":0.0,"publicationDate":"2011-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2012.625256","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59946457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 57

Social Influence and Evolution of Market Share 市场份额的社会影响与演变

Internet Mathematics Pub Date : 2011-03-30 DOI: 10.1080/15427951.2011.579849

Simla Ceyhan, M. Mousavi, A. Saberi

引用次数: 16

Estimating sizes of social networks via biased sampling 通过有偏抽样估计社交网络的规模

Internet Mathematics Pub Date : 2011-03-28 DOI: 10.1145/1963405.1963489

L. Katzir, Edo Liberty, O. Somekh, Ioana A. Cosma

{"title":"Estimating sizes of social networks via biased sampling","authors":"L. Katzir, Edo Liberty, O. Somekh, Ioana A. Cosma","doi":"10.1145/1963405.1963489","DOIUrl":"https://doi.org/10.1145/1963405.1963489","url":null,"abstract":"Online social networks have become very popular in recent years and their number of users is already measured in many hundreds of millions. For various commercial and sociological purposes, an independent estimate of their sizes is important. In this work, algorithms for estimating the number of users in such networks are considered. The proposed schemes are also applicable for estimating the sizes of networks' sub-populations. The suggested algorithms interact with the social networks via their public APIs only, and rely on no other external information. Due to obvious traffic and privacy concerns, the number of such interactions is severely limited. We therefore focus on minimizing the number of API interactions needed for producing good size estimates. We adopt the abstraction of social networks as undirected graphs and use random node sampling. By counting the number of collisions or non-unique nodes in the sample, we produce a size estimate. Then, we show analytically that the estimate error vanishes with high probability for smaller number of samples than those required by prior-art algorithms. Moreover, although our algorithms are provably correct for any graph, they excel when applied to social network-like graphs. The proposed algorithms were evaluated on synthetic as well real social networks such as Facebook, IMDB, and DBLP. Our experiments corroborated the theoretical results, and demonstrated the effectiveness of the algorithms.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"10 1","pages":"335 - 359"},"PeriodicalIF":0.0,"publicationDate":"2011-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/1963405.1963489","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64123853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 146