Studying Homophily Through Network Randomization
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Networks in Nature: Dynamics, Evolution, and Modularity
Networks in Nature: Dynamics, Evolution, and Modularity Sumeet Agarwal Merton College University of Oxford A thesis submitted for the degree of Doctor of Philosophy Hilary 2012 2 To my entire social network; for no man is an island Acknowledgements Primary thanks go to my supervisors, Nick Jones, Charlotte Deane, and Mason Porter, whose ideas and guidance have of course played a major role in shaping this thesis. I would also like to acknowledge the very useful sug- gestions of my examiners, Mark Fricker and Jukka-Pekka Onnela, which have helped improve this work. I am very grateful to all the members of the three Oxford groups I have had the fortune to be associated with: Sys- tems and Signals, Protein Informatics, and the Systems Biology Doctoral Training Centre. Their companionship has served greatly to educate and motivate me during the course of my time in Oxford. In particular, Anna Lewis and Ben Fulcher, both working on closely related D.Phil. projects, have been invaluable throughout, and have assisted and inspired my work in many different ways. Gabriel Villar and Samuel Johnson have been col- laborators and co-authors who have helped me to develop some of the ideas and methods used here. There are several other people who have gener- ously provided data, code, or information that has been directly useful for my work: Waqar Ali, Binh-Minh Bui-Xuan, Pao-Yang Chen, Dan Fenn, Katherine Huang, Patrick Kemmeren, Max Little, Aur´elienMazurie, Aziz Mithani, Peter Mucha, George Nicholson, Eli Owens, Stephen Reid, Nico- las Simonis, Dave Smith, Ian Taylor, Amanda Traud, and Jeffrey Wrana. -
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. -
Analysis of Topological Characteristics of Huge Online Social Networking Services Yong-Yeol Ahn, Seungyeop Han, Haewoon Kwak, Young-Ho Eom, Sue Moon, Hawoong Jeong
1 Analysis of Topological Characteristics of Huge Online Social Networking Services Yong-Yeol Ahn, Seungyeop Han, Haewoon Kwak, Young-Ho Eom, Sue Moon, Hawoong Jeong Abstract— Social networking services are a fast-growing busi- the statistics severely and it is imperative to use large data sets ness in the Internet. However, it is unknown if online relationships in network structure analysis. and their growth patterns are the same as in real-life social It is only very recently that we have seen research results networks. In this paper, we compare the structures of three online social networking services: Cyworld, MySpace, and orkut, from large networks. Novel network structures from human each with more than 10 million users, respectively. We have societies and communication systems have been unveiled; just access to complete data of Cyworld’s ilchon (friend) relationships to name a few are the Internet and WWW [3] and the patents, and analyze its degree distribution, clustering property, degree Autonomous Systems (AS), and affiliation networks [4]. Even correlation, and evolution over time. We also use Cyworld data in the short history of the Internet, SNSs are a fairly new to evaluate the validity of snowball sampling method, which we use to crawl and obtain partial network topologies of MySpace phenomenon and their network structures are not yet studied and orkut. Cyworld, the oldest of the three, demonstrates a carefully. The social networks of SNSs are believed to reflect changing scaling behavior over time in degree distribution. The the real-life social relationships of people more accurately than latest Cyworld data’s degree distribution exhibits a multi-scaling any other online networks. -
Modularity in Static and Dynamic Networks
Modularity in static and dynamic networks Sarah F. Muldoon University at Buffalo, SUNY OHBM – Brain Graphs Workshop June 25, 2017 Outline 1. Introduction: What is modularity? 2. Determining community structure (static networks) 3. Comparing community structure 4. Multilayer networks: Constructing multitask and temporal multilayer dynamic networks 5. Dynamic community structure 6. Useful references OHBM 2017 – Brain Graphs Workshop – Sarah F. Muldoon Introduction: What is Modularity? OHBM 2017 – Brain Graphs Workshop – Sarah F. Muldoon What is Modularity? Modularity (Community Structure) • A module (community) is a subset of vertices in a graph that have more connections to each other than to the rest of the network • Example social networks: groups of friends Modularity in the brain: • Structural networks: communities are groups of brain areas that are more highly connected to each other than the rest of the brain • Functional networks: communities are groups of brain areas with synchronous activity that is not synchronous with other brain activity OHBM 2017 – Brain Graphs Workshop – Sarah F. Muldoon Findings: The Brain is Modular Structural networks: cortical thickness correlations sensorimotor/spatial strategic/executive mnemonic/emotion olfactocentric auditory/language visual processing Chen et al. (2008) Cereb Cortex OHBM 2017 – Brain Graphs Workshop – Sarah F. Muldoon Findings: The Brain is Modular • Functional networks: resting state fMRI He et al. (2009) PLOS One OHBM 2017 – Brain Graphs Workshop – Sarah F. Muldoon Findings: The -
Oracle Database 10G: Oracle Spatial Network Data Model
Oracle Database 10g: Oracle Spatial Network Data Model An Oracle Technical White Paper May 2005 Oracle Spatial Network Data Model Table of Contents Introduction ....................................................................................................... 3 Design Goals and Architecture ....................................................................... 4 Major Steps Using the Network Data Model................................................ 5 Network Modeling........................................................................................ 5 Network Analysis.......................................................................................... 6 Network Modeling ............................................................................................ 6 Metadata and Schema ....................................................................................... 6 Network Java Representation and API.......................................................... 7 Network Creation Using SQL and PL/SQL ................................................ 8 Creating a Logical Network......................................................................... 9 Creating a Spatial Network.......................................................................... 9 Creating an SDO Geometry Network ................................................ 10 Creating an LRS Geometry Network.................................................. 10 Creating a Topology Geometry Network........................................... 11 Network Creation -
A Network-Of-Networks Percolation Analysis of Cascading Failures in Spatially Co-Located Road-Sewer Infrastructure Networks
Physica A 538 (2020) 122971 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa A network-of-networks percolation analysis of cascading failures in spatially co-located road-sewer infrastructure networks ∗ ∗ Shangjia Dong a, , Haizhong Wang a, , Alireza Mostafizi a, Xuan Song b a School of Civil and Construction Engineering, Oregon State University, Corvallis, OR 97331, United States of America b Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, China article info a b s t r a c t Article history: This paper presents a network-of-networks analysis framework of interdependent crit- Received 26 September 2018 ical infrastructure systems, with a focus on the co-located road-sewer network. The Received in revised form 28 May 2019 constructed interdependency considers two types of node dynamics: co-located and Available online 27 September 2019 multiple-to-one dependency, with different robustness metrics based on their function Keywords: logic. The objectives of this paper are twofold: (1) to characterize the impact of the Co-located road-sewer network interdependency on networks' robustness performance, and (2) to unveil the critical Network-of-networks percolation transition threshold of the interdependent road-sewer network. The results Percolation modeling show that (1) road and sewer networks are mutually interdependent and are vulnerable Infrastructure interdependency to the cascading failures initiated by sewer system disruption; (2) the network robust- Cascading failure ness decreases as the number of initial failure sources increases in the localized failure scenarios, but the rate declines as the number of failures increase; and (3) the sewer network contains two types of links: zero exposure and severe exposure to liquefaction, and therefore, it leads to a two-phase percolation transition subject to the probabilistic liquefaction-induced failures. -
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 -
Correlation in Complex Networks
Correlation in Complex Networks by George Tsering Cantwell A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) in the University of Michigan 2020 Doctoral Committee: Professor Mark Newman, Chair Professor Charles Doering Assistant Professor Jordan Horowitz Assistant Professor Abigail Jacobs Associate Professor Xiaoming Mao George Tsering Cantwell [email protected] ORCID iD: 0000-0002-4205-3691 © George Tsering Cantwell 2020 ACKNOWLEDGMENTS First, I must thank Mark Newman for his support and mentor- ship throughout my time at the University of Michigan. Further thanks are due to all of the people who have worked with me on projects related to this thesis. In alphabetical order they are Eliz- abeth Bruch, Alec Kirkley, Yanchen Liu, Benjamin Maier, Gesine Reinert, Maria Riolo, Alice Schwarze, Carlos Serván, Jordan Sny- der, Guillaume St-Onge, and Jean-Gabriel Young. ii TABLE OF CONTENTS Acknowledgments .................................. ii List of Figures ..................................... v List of Tables ..................................... vi List of Appendices .................................. vii Abstract ........................................ viii Chapter 1 Introduction .................................... 1 1.1 Why study networks?...........................2 1.1.1 Example: Modeling the spread of disease...........3 1.2 Measures and metrics...........................8 1.3 Models of networks............................ 11 1.4 Inference................................. -
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. -
Multidimensional Network Analysis
Universita` degli Studi di Pisa Dipartimento di Informatica Dottorato di Ricerca in Informatica Ph.D. Thesis Multidimensional Network Analysis Michele Coscia Supervisor Supervisor Fosca Giannotti Dino Pedreschi May 9, 2012 Abstract This thesis is focused on the study of multidimensional networks. A multidimensional network is a network in which among the nodes there may be multiple different qualitative and quantitative relations. Traditionally, complex network analysis has focused on networks with only one kind of relation. Even with this constraint, monodimensional networks posed many analytic challenges, being representations of ubiquitous complex systems in nature. However, it is a matter of common experience that the constraint of considering only one single relation at a time limits the set of real world phenomena that can be represented with complex networks. When multiple different relations act at the same time, traditional complex network analysis cannot provide suitable an- alytic tools. To provide the suitable tools for this scenario is exactly the aim of this thesis: the creation and study of a Multidimensional Network Analysis, to extend the toolbox of complex network analysis and grasp the complexity of real world phenomena. The urgency and need for a multidimensional network analysis is here presented, along with an empirical proof of the ubiquity of this multifaceted reality in different complex networks, and some related works that in the last two years were proposed in this novel setting, yet to be systematically defined. Then, we tackle the foundations of the multidimensional setting at different levels, both by looking at the basic exten- sions of the known model and by developing novel algorithms and frameworks for well-understood and useful problems, such as community discovery (our main case study), temporal analysis, link prediction and more. -
A Network Approach to Define Modularity of Components In
A Network Approach to Define Modularity of Components Manuel E. Sosa1 Technology and Operations Management Area, in Complex Products INSEAD, 77305 Fontainebleau, France Modularity has been defined at the product and system levels. However, little effort has e-mail: [email protected] gone into defining and quantifying modularity at the component level. We consider com- plex products as a network of components that share technical interfaces (or connections) Steven D. Eppinger in order to function as a whole and define component modularity based on the lack of Sloan School of Management, connectivity among them. Building upon previous work in graph theory and social net- Massachusetts Institute of Technology, work analysis, we define three measures of component modularity based on the notion of Cambridge, Massachusetts 02139 centrality. Our measures consider how components share direct interfaces with adjacent components, how design interfaces may propagate to nonadjacent components in the Craig M. Rowles product, and how components may act as bridges among other components through their Pratt & Whitney Aircraft, interfaces. We calculate and interpret all three measures of component modularity by East Hartford, Connecticut 06108 studying the product architecture of a large commercial aircraft engine. We illustrate the use of these measures to test the impact of modularity on component redesign. Our results show that the relationship between component modularity and component redesign de- pends on the type of interfaces connecting product components. We also discuss direc- tions for future work. ͓DOI: 10.1115/1.2771182͔ 1 Introduction The need to measure modularity has been highlighted implicitly by Saleh ͓12͔ in his recent invitation “to contribute to the growing Previous research on product architecture has defined modular- field of flexibility in system design” ͑p. -
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.