Internet Mathematics最新文献_第7页

Extracting the Core Structure of Social Networks Using (α, β)-Communities 利用(α， β)-社区提取社会网络核心结构

Internet Mathematics Pub Date : 2013-01-01 DOI: 10.1080/15427951.2012.678187

Liaoruo Wang, J. Hopcroft, Jing He, Hongyu Liang, Supasorn Suwajanakorn

引用次数: 13

High-Order Random Walks and Generalized Laplacians on Hypergraphs 超图上的高阶随机漫步和广义拉普拉斯算子

Internet Mathematics Pub Date : 2013-01-01 DOI: 10.1080/15427951.2012.678151

Linyuan Lu, Xing Peng

引用次数: 12

Discovery of Nodal Attributes through a Rank-Based Model of Network Structure 通过基于秩的网络结构模型发现节点属性

Internet Mathematics Pub Date : 2013-01-01 DOI: 10.1080/15427951.2012.678157

A. Henry, P. Prałat

引用次数: 3

Editorial Board EOV 编辑委员会EOV

Internet Mathematics Pub Date : 2012-12-01 DOI: 10.1080/15427951.2012.748407

引用次数: 0

Bistability through Triadic Closure 通过三元闭包实现双稳定性

Internet Mathematics Pub Date : 2012-12-01 DOI: 10.1080/15427951.2012.714718

P. Grindrod, D. Higham, Mark C. Parsons

{"title":"Bistability through Triadic Closure","authors":"P. Grindrod, D. Higham, Mark C. Parsons","doi":"10.1080/15427951.2012.714718","DOIUrl":"https://doi.org/10.1080/15427951.2012.714718","url":null,"abstract":"We propose and analyze a class of evolving network models suitable for describing a dynamic topological structure. Applications include telecommunication, online social behavior, and information processing in neuroscience. We model the evolving network as a discrete-time Markov chain and study a very general framework in which edges conditioned on the current state appear or disappear independently at the next time step. We show how to exploit symmetries in the microscopic, localized rules in order to obtain conjugate classes of random graphs that simplify analysis and calibration of a model. Further, we develop a mean field theory for describing network evolution. For a simple but realistic scenario incorporating the triadic closure effect that has been empirically observed by social scientists (friends of friends tend to become friends), the mean field theory predicts bistable dynamics, and computational results confirm this prediction. We also discuss the calibration issue for a set of real cellphone data, and find support for a block model in which individuals are assigned to one of two distinct groups having different within-group and across-group dynamics.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"60 1","pages":"402 - 423"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2012.714718","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59947164","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: 18

Balance in Random Signed Graphs 随机符号图中的平衡

Internet Mathematics Pub Date : 2012-12-01 DOI: 10.1080/15427951.2012.675413

A. E. Maftouhi, Y. Manoussakis, O. Megalakaki

{"title":"Balance in Random Signed Graphs","authors":"A. E. Maftouhi, Y. Manoussakis, O. Megalakaki","doi":"10.1080/15427951.2012.675413","DOIUrl":"https://doi.org/10.1080/15427951.2012.675413","url":null,"abstract":"By extending Heider’s and Cartwright–Harary’s theory of balance in deterministic social structures, we study the problem of balance in social structures in which relations among individuals are random. An appropriate model for representing such structures is that of random signed graphs G n,p,q , defined as follows. Given a set of n vertices and fixed numbers p and q, 0<p+q<1, then between each pair of vertices, there exists a positive edge, a negative edge, or no edge with respective probabilities p, q, 1−p−q. We first show that almost always (i.e., with probability tending to 1 as n→∞), the random signed graph G n,p,q is unbalanced. Subsequently we estimate the maximum order of a balanced induced subgraph in G n,p,p and show that its order achieves only a finite number of values. Next, we study the asymptotic behavior of the degree of balance and give upper and lower bounds for the line index of balance. Finally, we study the threshold function of balance, e.g., a function p 0(n) such that if p≫p 0(n), then the random signed graph G n,p,p is almost always unbalanced, and otherwise, it is almost always balanced.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"8 1","pages":"364 - 380"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2012.675413","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59946861","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: 9

Mean Commute Time for Random Walks on Hierarchical Scale-Free Networks 分层无标度网络随机行走的平均通勤时间

Internet Mathematics Pub Date : 2012-12-01 DOI: 10.1080/15427951.2012.685685

Y. Shang

引用次数: 17

Digraph Laplacian and the Degree of Asymmetry 有向图拉普拉斯算子与不对称度

Internet Mathematics Pub Date : 2012-12-01 DOI: 10.1080/15427951.2012.708890

Yanhua Li, Zhi-Li Zhang

{"title":"Digraph Laplacian and the Degree of Asymmetry","authors":"Yanhua Li, Zhi-Li Zhang","doi":"10.1080/15427951.2012.708890","DOIUrl":"https://doi.org/10.1080/15427951.2012.708890","url":null,"abstract":"In this paper we extend and generalize the standard spectral graph theory (or random-walk theory) on undirected graphs to digraphs. In particular, we introduce and define a normalized digraph Laplacian (Diplacian for short) Γ for digraphs, and prove that (1) its Moore–Penrose pseudoinverse is the discrete Green’s function of the Diplacian matrix as an operator on digraphs, and (2) it is the normalized fundamental matrix of the Markov chain governing random walks on digraphs. Using these results, we derive a new formula for computing hitting and commute times in terms of the Moore–Penrose pseudoinverse of the Diplacian, or equivalently, the singular values and vectors of the Diplacian. Furthermore, we show that the Cheeger constant defined in [Chung 05] is intrinsically a quantity associated with undirected graphs. This motivates us to introduce a metric, the largest singular value of the skewed Laplacian ∇=(Γ−Γ T )/2, to quantify and measure the degree of asymmetry in a digraph. Using this measure, we establish several new results, such as a tighter bound than that in [Chung 05] on the Markov chain mixing rate, and a bound on the second-smallest singular value of Γ.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"8 1","pages":"381 - 401"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2012.708890","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59947114","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: 58

Approximations of the Generalized Inverse of the Graph Laplacian Matrix 图拉普拉斯矩阵广义逆的近似

Internet Mathematics Pub Date : 2012-12-01 DOI: 10.1080/15427951.2012.715115

E. Bozzo, Massimo Franceschet

{"title":"Approximations of the Generalized Inverse of the Graph Laplacian Matrix","authors":"E. Bozzo, Massimo Franceschet","doi":"10.1080/15427951.2012.715115","DOIUrl":"https://doi.org/10.1080/15427951.2012.715115","url":null,"abstract":"We devise methods for finding approximations of the generalized inverse of the graph Laplacian matrix, which arises in many graph-theoretic applications. Finding this matrix in its entirety involves solving a matrix inversion problem, which is resource-demanding in terms of consumed time and memory and hence impractical whenever the graph is relatively large. Our approximations use only a few eigenpairs of the Laplacian matrix and are parametric with respect to this number, so that the user can compromise between effectiveness and efficiency of the approximate solution. We apply the devised approximations to the problem of computing current-flow betweenness centrality on a graph. However, given the generality of the Laplacian matrix, many other applications can be sought. We experimentally demonstrate that the approximations are effective already with a constant number of eigenpairs. These few eigenpairs can be stored with a linear amount of memory in the number of nodes of the graph, and in the realistic case of sparse networks, they can be efficiently computed using one of the many methods for retrieving a few eigenpairs of sparse matrices that abound in the literature.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"8 1","pages":"456 - 481"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2012.715115","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59947170","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: 20

Model Selection for Social Networks Using Graphlets 使用Graphlets的社交网络模型选择

Internet Mathematics Pub Date : 2012-12-01 DOI: 10.1080/15427951.2012.671149

J. Janssen, Matt Hurshman, N. Kalyaniwalla

引用次数: 54