Beyond Distance Decay: Discover Homophily in Spatially Embedded Social Networks
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Geodesic Distance Descriptors
Geodesic Distance Descriptors Gil Shamai and Ron Kimmel Technion - Israel Institute of Technologies [email protected] [email protected] Abstract efficiency of state of the art shape matching procedures. The Gromov-Hausdorff (GH) distance is traditionally used for measuring distances between metric spaces. It 1. Introduction was adapted for non-rigid shape comparison and match- One line of thought in shape analysis considers an ob- ing of isometric surfaces, and is defined as the minimal ject as a metric space, and object matching, classification, distortion of embedding one surface into the other, while and comparison as the operation of measuring the discrep- the optimal correspondence can be described as the map ancies and similarities between such metric spaces, see, for that minimizes this distortion. Solving such a minimiza- example, [13, 33, 27, 23, 8, 3, 24]. tion is a hard combinatorial problem that requires pre- Although theoretically appealing, the computation of computation and storing of all pairwise geodesic distances distances between metric spaces poses complexity chal- for the matched surfaces. A popular way for compact repre- lenges as far as direct computation and memory require- sentation of functions on surfaces is by projecting them into ments are involved. As a remedy, alternative representa- the leading eigenfunctions of the Laplace-Beltrami Opera- tion spaces were proposed [26, 22, 15, 10, 31, 30, 19, 20]. tor (LBO). When truncated, the basis of the LBO is known The question of which representation to use in order to best to be the optimal for representing functions with bounded represent the metric space that define each form we deal gradient in a min-max sense. -
Corporate Competition: a Self-Organized Network
Corporate Competition: A Self-Organized Network Dan Braha New England Complex Systems Institute, Cambridge, Massachusetts and University of Massachusetts, Dartmouth, Massachusetts Blake Stacey and Yaneer Bar-Yam New England Complex Systems Institute, Cambridge, Massachusetts Please cite this article in press as: Braha, D., Stacey, B., and Bar-Yam, Y. Corporate competition: A self- organized network. Social Networks (2011), doi:10.1016/j.socnet.2011.05.004 A substantial number of studies have extended the work on universal properties in physical systems to complex networks in social, biological, and technological systems. In this paper, we present a complex networks perspective on interfirm organizational networks by mapping, analyzing and modeling the spatial structure of a large interfirm competition network across a variety of sectors and industries within the United States. We propose two micro-dynamic models that are able to reproduce empirically observed characteristics of competition networks as a natural outcome of a minimal set of general mechanisms governing the formation of competition networks. Both models, which utilize different approaches yet apply common principles to network formation give comparable results. There is an asymmetry between companies that are considered competitors, and companies that consider others as their competitors. All companies only consider a small number of other companies as competitors; however, there are a few companies that are considered as competitors by many others. Geographically, the density of corporate headquarters strongly correlates with local population density, and the probability two firms are competitors declines with geographic distance. We construct these properties by growing a corporate network with competitive links using random incorporations modulated by population density and geographic distance. -
Network Science
This is a preprint of Katy Börner, Soma Sanyal and Alessandro Vespignani (2007) Network Science. In Blaise Cronin (Ed) Annual Review of Information Science & Technology, Volume 41. Medford, NJ: Information Today, Inc./American Society for Information Science and Technology, chapter 12, pp. 537-607. Network Science Katy Börner School of Library and Information Science, Indiana University, Bloomington, IN 47405, USA [email protected] Soma Sanyal School of Library and Information Science, Indiana University, Bloomington, IN 47405, USA [email protected] Alessandro Vespignani School of Informatics, Indiana University, Bloomington, IN 47406, USA [email protected] 1. Introduction.............................................................................................................................................2 2. Notions and Notations.............................................................................................................................4 2.1 Graphs and Subgraphs .........................................................................................................................5 2.2 Graph Connectivity..............................................................................................................................7 3. Network Sampling ..................................................................................................................................9 4. Network Measurements........................................................................................................................11 -
Latent Distance Estimation for Random Geometric Graphs ∗
Latent Distance Estimation for Random Geometric Graphs ∗ Ernesto Araya Valdivia Laboratoire de Math´ematiquesd'Orsay (LMO) Universit´eParis-Sud 91405 Orsay Cedex France Yohann De Castro Ecole des Ponts ParisTech-CERMICS 6 et 8 avenue Blaise Pascal, Cit´eDescartes Champs sur Marne, 77455 Marne la Vall´ee,Cedex 2 France Abstract: Random geometric graphs are a popular choice for a latent points generative model for networks. Their definition is based on a sample of n points X1;X2; ··· ;Xn on d−1 the Euclidean sphere S which represents the latent positions of nodes of the network. The connection probabilities between the nodes are determined by an unknown function (referred to as the \link" function) evaluated at the distance between the latent points. We introduce a spectral estimator of the pairwise distance between latent points and we prove that its rate of convergence is the same as the nonparametric estimation of a d−1 function on S , up to a logarithmic factor. In addition, we provide an efficient spectral algorithm to compute this estimator without any knowledge on the nonparametric link function. As a byproduct, our method can also consistently estimate the dimension d of the latent space. MSC 2010 subject classifications: Primary 68Q32; secondary 60F99, 68T01. Keywords and phrases: Graphon model, Random Geometric Graph, Latent distances estimation, Latent position graph, Spectral methods. 1. Introduction Random geometric graph (RGG) models have received attention lately as alternative to some simpler yet unrealistic models as the ubiquitous Erd¨os-R´enyi model [11]. They are generative latent point models for graphs, where it is assumed that each node has associated a latent d point in a metric space (usually the Euclidean unit sphere or the unit cube in R ) and the connection probability between two nodes depends on the position of their associated latent points. -
Average D-Distance Between Vertices of a Graph
italian journal of pure and applied mathematics { n. 33¡2014 (293¡298) 293 AVERAGE D-DISTANCE BETWEEN VERTICES OF A GRAPH D. Reddy Babu Department of Mathematics Koneru Lakshmaiah Education Foundation (K.L. University) Vaddeswaram Guntur 522 502 India e-mail: [email protected], [email protected] P.L.N. Varma Department of Science & Humanities V.F.S.T.R. University Vadlamudi Guntur 522 237 India e-mail: varma [email protected] Abstract. The D-distance between vertices of a graph G is obtained by considering the path lengths and as well as the degrees of vertices present on the path. The average D-distance between the vertices of a connected graph is the average of the D-distances between all pairs of vertices of the graph. In this article we study the average D-distance between the vertices of a graph. Keywords: D-distance, average D-distance, diameter. 2000 Mathematics Subject Classi¯cation: 05C12. 1. Introduction The concept of distance is one of the important concepts in study of graphs. It is used in isomorphism testing, graph operations, hamiltonicity problems, extremal problems on connectivity and diameter, convexity in graphs etc. Distance is the basis of many concepts of symmetry in graphs. In addition to the usual distance, d(u; v) between two vertices u; v 2 V (G) we have detour distance (introduced by Chartrand et al, see [2]), superior distance (introduced by Kathiresan and Marimuthu, see [6]), signal distance (introduced by Kathiresan and Sumathi, see [7]), degree distance etc. 294 d. reddy babu, p.l.n. varma In an earlier article [9], the authors introduced the concept of D-distance be- tween vertices of a graph G by considering not only path length between vertices, but also the degrees of all vertices present in a path while de¯ning the D-distance. -
"Distance Measures for Graph Theory"
Distance measures for graph theory : Comparisons and analyzes of different methods Dissertation presented by Maxime DUYCK for obtaining the Master’s degree in Mathematical Engineering Supervisor(s) Marco SAERENS Reader(s) Guillaume GUEX, Bertrand LEBICHOT Academic year 2016-2017 Acknowledgments First, I would like to thank my supervisor Pr. Marco Saerens for his presence, his advice and his precious help throughout the realization of this thesis. Second, I would also like to thank Bertrand Lebichot and Guillaume Guex for agreeing to read this work. Next, I would like to thank my parents, all my family and my friends to have accompanied and encouraged me during all my studies. Finally, I would thank Malian De Ron for creating this template [65] and making it available to me. This helped me a lot during “le jour et la nuit”. Contents 1. Introduction 1 1.1. Context presentation .................................. 1 1.2. Contents .......................................... 2 2. Theoretical part 3 2.1. Preliminaries ....................................... 4 2.1.1. Networks and graphs .............................. 4 2.1.2. Useful matrices and tools ........................... 4 2.2. Distances and kernels on a graph ........................... 7 2.2.1. Notion of (dis)similarity measures ...................... 7 2.2.2. Kernel on a graph ................................ 8 2.2.3. The shortest-path distance .......................... 9 2.3. Kernels from distances ................................. 9 2.3.1. Multidimensional scaling ............................ 9 2.3.2. Gaussian mapping ............................... 9 2.4. Similarity measures between nodes .......................... 9 2.4.1. Katz index and its Leicht’s extension .................... 10 2.4.2. Commute-time distance and Euclidean commute-time distance .... 10 2.4.3. SimRank similarity measure ......................... -
Percolation Theory Are Well-Suited To
Models of Disordered Media and Predictions of Associated Hydraulic Conductivity A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science By L AARON BLANK B.S., Wright State University, 2004 2006 Wright State University WRIGHT STATE UNIVERSITY SCHOOL OF GRADUATE STUDIES Novermber 6, 2006 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY L Blank ENTITLED Models of Disordered Media and Predictions of Associated Hydraulic Conductivity BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science. _______________________ Allen Hunt, Ph.D. Thesis Advisor _______________________ Lok Lew Yan Voon, Ph.D. Department Chair _______________________ Joseph F. Thomas, Jr., Ph.D. Dean of the School of Graduate Studies Committee on Final Examination ____________________ Allen Hunt, Ph.D. ____________________ Brent D. Foy, Ph.D. ____________________ Gust Bambakidis, Ph.D. ____________________ Thomas Skinner, Ph.D. Abstract In the late 20th century there was a spill of Technetium in eastern Washington State at the US Department of Energy Hanford site. Resulting contamination of water supplies would raise serious health issues for local residents. Therefore, the ability to predict how these contaminants move through the soil is of great interest. The main contribution to contaminant transport arises from being carried along by flowing water. An important control on the movement of the water through the medium is the hydraulic conductivity, K, which defines the ease of water flow for a given pressure difference (analogous to the electrical conductivity). The overall goal of research in this area is to develop a technique which accurately predicts the hydraulic conductivity as well as its distribution, both in the horizontal and the vertical directions, for media representative of the Hanford subsurface. -
Practice Exam 1
PRACTICE EXAM 1 AP Human Geography Section I TIME: 60 minutes 75 multiple-choice questions (Answer sheets appear in the back of this book.) Directions: Each of the following questions is followed by five suggested answers or completions. Select the best answer choice. 1. All the following have been considered new industrial countries EXCEPT (A) Hong Kong (D) China (B) South Korea (E) Indonesia (C) Brazil 2. Which of the following is an example of a quinary-sector economic activity? (A) Working at a cash register at McDonald’s (B) Serving as a researcher for human genetic cloning (C) Serving on the U.S. president’s cabinet (D) Converting crude oil into gasoline (E) Plowing land in preparation for planting a crop 3. London has become a world city in part because of its proximity to ports and other places that foster development. This reason for London’s historic growth relates to the city’s (A) site (D) situation (B) sovereignty (E) distance decay (C) redlining 4. Which of the following is a valid difference between the urban patterns of the United States and those of Latin America? (A) Unlike U.S. cities, Latin American cities have ghettos. (B) U.S cities follow a sector pattern, whereas Latin American cities follow concentric zones. (C) Gentrification is more present in Latin American cities. (D) Latin American cities have more-defined industrial sectors. (E) Unlike U.S. cities, Latin American cities show patterns of wealthy residents emanating from the city’s central business district. 5. The number of people under the age of 15 plus the number of people above the age of 64 divided by the number of the people aged 15 through 64 is defined as (A) carrying capacity (D) age-sex pyramid (B) primary economic sector (E) infrastructure (C) dependency ratio 6. -
Regional Development and the New Economy
A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Gillespie, Andrew; Richardson, Ranald; Cornford, James Article Regional development and the new economy EIB Papers Provided in Cooperation with: European Investment Bank (EIB), Luxembourg Suggested Citation: Gillespie, Andrew; Richardson, Ranald; Cornford, James (2001) : Regional development and the new economy, EIB Papers, ISSN 0257-7755, European Investment Bank (EIB), Luxembourg, Vol. 6, Iss. 1, pp. 109-131 This Version is available at: http://hdl.handle.net/10419/44801 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. www.econstor.eu Regional development and the new economy 1. Introduction In this paper we are concerned with the implications of information and communications technologies (ICTs), and the so-called “new economy” with which they are associated, for regional development. -
Sex, Race, Religion, Age, and Education Homophily Among Confidants, 1985 to 2004 Jeffrey A
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Sociology Department, Faculty Publications Sociology, Department of 4-2014 Social Distance in the United States: Sex, Race, Religion, Age, and Education Homophily among Confidants, 1985 to 2004 Jeffrey A. Smith University of Nebraska-Lincoln, [email protected] Miller McPherson Duke University, [email protected] Lynn Smith-Lovin Duke University, [email protected] Follow this and additional works at: http://digitalcommons.unl.edu/sociologyfacpub Part of the Demography, Population, and Ecology Commons, Race and Ethnicity Commons, Social Psychology and Interaction Commons, and the Social Statistics Commons Smith, Jeffrey A.; McPherson, Miller; and Smith-Lovin, Lynn, "Social Distance in the United States: Sex, Race, Religion, Age, and Education Homophily among Confidants, 1985 to 2004" (2014). Sociology Department, Faculty Publications. 246. http://digitalcommons.unl.edu/sociologyfacpub/246 This Article is brought to you for free and open access by the Sociology, Department of at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Sociology Department, Faculty Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Published in American Sociological Review 79:3 (2014), pp. 432-456. doi: 10.1177/0003122414531776 Copyright © 2014 American Sociological Review. Used by permission. digitalcommons.unl.edu Published online April 24, 2014. Social Distance in the United States: Sex, Race, Religion, Age, and Education Homophily among Confidants, 1985 to 2004 Jeffrey A. Smith,1 Miller McPherson,2 and Lynn Smith-Lovin2 1. University of Nebraska-Lincoln 2. Duke University Corresponding author – Jeffrey A. Smith, Department of Sociology, University of Nebraska-Lincoln, 711 Oldfather Hall, Lincoln, NE 68588-0324, email [email protected] Abstract Homophily, the tendency for similar actors to be connected at a higher rate than dissimi- lar actors, is a pervasive social fact. -
Assortativity Measures for Weighted and Directed Networks
Assortativity measures for weighted and directed networks Yelie Yuan1, Jun Yan1, and Panpan Zhang2,∗ 1Department of Statistics, University of Connecticut, Storrs, CT 06269 2Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania, Philadelphia, PA 19104 ∗Corresponding author: [email protected] January 15, 2021 arXiv:2101.05389v1 [stat.AP] 13 Jan 2021 Abstract Assortativity measures the tendency of a vertex in a network being connected by other ver- texes with respect to some vertex-specific features. Classical assortativity coefficients are defined for unweighted and undirected networks with respect to vertex degree. We propose a class of assortativity coefficients that capture the assortative characteristics and structure of weighted and directed networks more precisely. The vertex-to-vertex strength correlation is used as an example, but the proposed measure can be applied to any pair of vertex-specific features. The effectiveness of the proposed measure is assessed through extensive simula- tions based on prevalent random network models in comparison with existing assortativity measures. In application World Input-Ouput Networks, the new measures reveal interesting insights that would not be obtained by using existing ones. An implementation is publicly available in a R package wdnet. 1 Introduction In traditional network analysis, assortativity or assortative mixing (Newman, 2002) is a mea- sure assessing the preference of a vertex being connected (by edges) with other vertexes in a network. The measure reflects the principle of homophily (McPherson et al., 2001)|the tendency of the entities to be associated with similar partners in a social network. The prim- itive assortativity measure proposed by Newman(2002) was defined to study the tendency of connections between nodes based on their degrees, which is why it is also called degree-degree correlation (van der Hofstad and Litvak, 2014). -
The Review of Regional Studies
http://www.diva-portal.org This is the published version of a paper published in The Review of Regional Studies. Citation for the original published paper (version of record): Klaesson, J., Öner, Ö. (2014) Market reach for retail services. The Review of Regional Studies, 44(2): 153-176 Access to the published version may require subscription. N.B. When citing this work, cite the original published paper. Open Access journal: http://journal.srsa.org/ojs/index.php/RRS/ Permanent link to this version: http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-23749 (2014) 44, 153–176 The Review of Regional Studies The Official Journal of the Southern Regional Science Association Market Reach for Retail Services* Johan Klaessona and Özge Önera,b aCentre for Entrepreneurship and Spatial Economics, Jönköping International Business School, Sweden bResearch Institute of Industrial Economics, Sweden Abstract: Retail is concentrated in areas where demand is high. A measure of market potential can be used to calculate place-specific demand for retail services. The effect of distance on market potential depends on the willingness of consumers to travel for the products they purchase. The spatial reach of demand is frequently operationalized using a distance-decay function. The purpose of this paper is to estimate such distance-decay functions for different branches of the retail sector. The paper uses spatial data from the Stockholm region in Sweden. The results indicate that, in line with theory, there are indeed differences in the distance decay of demand among retail subsectors. Keywords: retail, market potential, distance-decay JEL Codes: L81, P25, R12 1.