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Group-In-A-Box Layout for Multi-Faceted Analysis of Communities
2011 IEEE International Conference on Privacy, Security, Risk, and Trust, and IEEE International Conference on Social Computing Group-In-a-Box Layout for Multi-faceted Analysis of Communities Eduarda Mendes Rodrigues*, Natasa Milic-Frayling †, Marc Smith‡, Ben Shneiderman§, Derek Hansen¶ * Dept. of Informatics Engineering, Faculty of Engineering, University of Porto, Portugal [email protected] † Microsoft Research, Cambridge, UK [email protected] ‡ Connected Action Consulting Group, Belmont, California, USA [email protected] § Dept. of Computer Science & Human-Computer Interaction Lab University of Maryland, College Park, Maryland, USA [email protected] ¶ College of Information Studies & Center for the Advanced Study of Communities and Information University of Maryland, College Park, Maryland, USA [email protected] Abstract—Communities in social networks emerge from One particularly important aspect of social network interactions among individuals and can be analyzed through a analysis is the detection of communities, i.e., sub-groups of combination of clustering and graph layout algorithms. These individuals or entities that exhibit tight interconnectivity approaches result in 2D or 3D visualizations of clustered among the wider population. For example, Twitter users who graphs, with groups of vertices representing individuals that regularly retweet each other’s messages may form cohesive form a community. However, in many instances the vertices groups within the Twitter social network. In a network have attributes that divide individuals into distinct categories visualization they would appear as clusters or sub-graphs, such as gender, profession, geographic location, and similar. It often colored distinctly or represented by a different vertex is often important to investigate what categories of individuals shape in order to convey their group identity. -
Joint Estimation of Preferential Attachment and Node Fitness In
www.nature.com/scientificreports OPEN Joint estimation of preferential attachment and node fitness in growing complex networks Received: 15 April 2016 Thong Pham1, Paul Sheridan2 & Hidetoshi Shimodaira1 Accepted: 09 August 2016 Complex network growth across diverse fields of science is hypothesized to be driven in the main by Published: 07 September 2016 a combination of preferential attachment and node fitness processes. For measuring the respective influences of these processes, previous approaches make strong and untested assumptions on the functional forms of either the preferential attachment function or fitness function or both. We introduce a Bayesian statistical method called PAFit to estimate preferential attachment and node fitness without imposing such functional constraints that works by maximizing a log-likelihood function with suitably added regularization terms. We use PAFit to investigate the interplay between preferential attachment and node fitness processes in a Facebook wall-post network. While we uncover evidence for both preferential attachment and node fitness, thus validating the hypothesis that these processes together drive complex network evolution, we also find that node fitness plays the bigger role in determining the degree of a node. This is the first validation of its kind on real-world network data. But surprisingly the rate of preferential attachment is found to deviate from the conventional log-linear form when node fitness is taken into account. The proposed method is implemented in the R package PAFit. The study of complex network evolution is a hallmark of network science. Research in this discipline is inspired by empirical observations underscoring the widespread nature of certain structural features, such as the small-world property1, a high clustering coefficient2, a heavy tail in the degree distribution3, assortative mixing patterns among nodes4, and community structure5 in a multitude of biological, societal, and technological networks6–11. -
Lecture 20 — March 20, 2013 1 the Maximum Cut Problem 2 a Spectral
UBC CPSC 536N: Sparse Approximations Winter 2013 Lecture 20 | March 20, 2013 Prof. Nick Harvey Scribe: Alexandre Fr´echette We study the Maximum Cut Problem with approximation in mind, and naturally we provide a spectral graph theoretic approach. 1 The Maximum Cut Problem Definition 1.1. Given a (undirected) graph G = (V; E), the maximum cut δ(U) for U ⊆ V is the cut with maximal value jδ(U)j. The Maximum Cut Problem consists of finding a maximal cut. We let MaxCut(G) = maxfjδ(U)j : U ⊆ V g be the value of the maximum cut in G, and 0 MaxCut(G) MaxCut = jEj be the normalized version (note that both normalized and unnormalized maximum cut values are induced by the same set of nodes | so we can interchange them in our search for an actual maximum cut). The Maximum Cut Problem is NP-hard. For a long time, the randomized algorithm 1 1 consisting of uniformly choosing a cut was state-of-the-art with its 2 -approximation factor The simplicity of the algorithm and our inability to find a better solution were unsettling. Linear pro- gramming unfortunately didn't seem to help. However, a (novel) technique called semi-definite programming provided a 0:878-approximation algorithm [Goemans-Williamson '94], which is optimal assuming the Unique Games Conjecture. 2 A Spectral Approximation Algorithm Today, we study a result of [Trevison '09] giving a spectral approach to the Maximum Cut Problem with a 0:531-approximation factor. We will present a slightly simplified result with 0:5292-approximation factor. -
Networkx Reference Release 1.9.1
NetworkX Reference Release 1.9.1 Aric Hagberg, Dan Schult, Pieter Swart September 20, 2014 CONTENTS 1 Overview 1 1.1 Who uses NetworkX?..........................................1 1.2 Goals...................................................1 1.3 The Python programming language...................................1 1.4 Free software...............................................2 1.5 History..................................................2 2 Introduction 3 2.1 NetworkX Basics.............................................3 2.2 Nodes and Edges.............................................4 3 Graph types 9 3.1 Which graph class should I use?.....................................9 3.2 Basic graph types.............................................9 4 Algorithms 127 4.1 Approximation.............................................. 127 4.2 Assortativity............................................... 132 4.3 Bipartite................................................. 141 4.4 Blockmodeling.............................................. 161 4.5 Boundary................................................. 162 4.6 Centrality................................................. 163 4.7 Chordal.................................................. 184 4.8 Clique.................................................. 187 4.9 Clustering................................................ 190 4.10 Communities............................................... 193 4.11 Components............................................... 194 4.12 Connectivity.............................................. -
Facing the Future: European Research Infrastructures for the Humanities and Social Sciences
Facing the Future: European Research Infrastructures for the Humanities and Social Sciences Adrian Duşa, Dietrich Nelle, Günter Stock, and Gert G. Wagner (Eds.) Facing the Future: European Research Infrastructures for the Humanities and Social Sciences E d i t o r s : Adrian Duşa (SCI-SWG), Dietrich Nelle (BMBF), Günter Stock (ALLEA), and Gert. G. Wagner (RatSWD) ISBN 978-3-944417-03-5 1st edition © 2014 SCIVERO Verlag, Berlin SCIVERO is a trademark of GWI Verwaltungsgesellschaft für Wissenschaftspoli- tik und Infrastrukturentwicklung Berlin UG (haftungsbeschränkt). This book documents the results of the conference Facing the Future: European Research Infrastructure for Humanities and Social Sciences (November 21/22 2013, Berlin), initiated by the Social and Cultural Innovation Strategy Work- ing Group of ESFRI (SCI-SWG) and the German Federal Ministry of Education and Research (BMBF), and hosted by the European Federation of Academies of Sciences and Humanities (ALLEA) and the German Data Forum (RatSWD). Thanks and appreciation are due to all authors, speakers and participants of the conference, and all involved institutions, in particular the German Federal Ministry of Education and Research (BMBF). The ministry funded the conference and this subsequent publication as part of the Union of the German Academies of Sciences and Humanities’ project “Survey and Analysis of Basic Humanities and Social Science Research at the Science Academies Related Research Insti- tutes of Europe”. The views expressed in this publication are exclusively the opinions of the authors and not those of the German Federal Ministry of Education and Research. Editing: Dominik Adrian, Camilla Leathem, Thomas Runge, Simon Wolff Layout and graphic design: Thomas Runge Contents Preface . -
Synthetic Graph Generation for Data-Intensive HPC Benchmarking: Background and Framework
ORNL/TM-2013/339 Synthetic Graph Generation for Data-Intensive HPC Benchmarking: Background and Framework October 2013 Prepared by Joshua Lothian, Sarah Powers, Blair D. Sullivan, Matthew Baker, Jonathan Schrock, Stephen W. Poole DOCUMENT AVAILABILITY Reports produced after January 1, 1996, are generally available free via the U.S. Department of Energy (DOE) Information Bridge: Web Site: http://www.osti.gov/bridge Reports produced before January 1, 1996, may be purchased by members of the public from the following source: National Technical Information Service 5285 Port Royal Road Springfield, VA 22161 Telephone: 703-605-6000 (1-800-553-6847) TDD: 703-487-4639 Fax: 703-605-6900 E-mail: [email protected] Web site: http://www.ntis.gov/support/ordernowabout.htm Reports are available to DOE employees, DOE contractors, Energy Technology Data Ex- change (ETDE), and International Nuclear Information System (INIS) representatives from the following sources: Office of Scientific and Technical Information P.O. Box 62 Oak Ridge, TN 37831 Telephone: 865-576-8401 Fax: 865-576-5728 E-mail: [email protected] Web site:http://www.osti.gov/contact.html This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or other- wise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. -
Extracting Insights from Differences: Analyzing Node-Aligned Social
Extracting Insights from Differences: Analyzing Node-aligned Social Graphs by Srayan Datta A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Computer Science and Engineering) in The University of Michigan 2019 Doctoral Committee: Associate Professor Eytan Adar, Chair Associate Professor Mike Cafarella Assistant Professor Danai Koutra Associate Professor Clifford Lampe Srayan Datta [email protected] ORCID iD: 0000-0002-5800-830X c Srayan Datta 2019 To my family and friends ii ACKNOWLEDGEMENTS There are several people who made this dissertation possible, first among this long list is my adviser, Eytan Adar. Pursuing a doctoral program after just finishing un- dergraduate studies can be a daunting task but Eytan made it easy with his patience, kindness, and guidance. I learned a lot from our collaborations and idle conversations and I am very grateful for that. I would like to extend my thanks to the rest of my thesis committee, Mike Ca- farella, Danai Koutra and Cliff Lampe for their suggestions and constructive feed- back. I would also like to thank the following faculty members, Daniel Romero, Ceren Budak, Eric Gilbert and David Jurgens for their long insightful conversations and suggestions about some of my projects. I would like to thank all of friends and colleagues who helped (as a co-author or through critique) or supported me through this process. This is an enormous list but I am especially thankful to Chanda Phelan, Eshwar Chandrasekharan, Sam Carton, Cristina Garbacea, Shiyan Yan, Hari Subramonyam, Bikash Kanungo, and Ram Srivatasa. I would like to thank my parents for their unwavering support and faith in me. -
Preferential Attachment Model with Degree Bound and Its Application to Key Predistribution in WSN
Preferential Attachment Model with Degree Bound and its Application to Key Predistribution in WSN Sushmita Rujy and Arindam Palz y Indian Statistical Institute, Kolkata, India. Email: [email protected] z TCS Innovation Labs, Kolkata, India. Email: [email protected] Abstract—Preferential attachment models have been widely particularly those in the military domain [14]. The resource studied in complex networks, because they can explain the constrained nature of sensors restricts the use of public key formation of many networks like social networks, citation methods to secure communication. Key predistribution [7] networks, power grids, and biological networks, to name a few. Motivated by the application of key predistribution in wireless is a widely used symmetric key management technique in sensor networks (WSN), we initiate the study of preferential which cryptographic keys are preloaded in sensor networks attachment with degree bound. prior to deployment. Sensor nodes find out the common keys Our paper has two important contributions to two different using a shared key discovery phase. Messages are encrypted areas. The first is a contribution in the study of complex by the source node using the shared key and decrypted at the networks. We propose preferential attachment model with degree bound for the first time. In the normal preferential receiving node using the same key. attachment model, the degree distribution follows a power law, The number of keys in each node is to be minimized, in with many nodes of low degree and a few nodes of high degree. order to reduce storage space. Direct communication between In our scheme, the nodes can have a maximum degree dmax, any pair of nodes help in quick and easy transmission of where dmax is an integer chosen according to the application. -
Network Analysis with Nodexl
Social data: Advanced Methods – Social (Media) Network Analysis with NodeXL A project from the Social Media Research Foundation: http://www.smrfoundation.org About Me Introductions Marc A. Smith Chief Social Scientist Connected Action Consulting Group [email protected] http://www.connectedaction.net http://www.codeplex.com/nodexl http://www.twitter.com/marc_smith http://delicious.com/marc_smith/Paper http://www.flickr.com/photos/marc_smith http://www.facebook.com/marc.smith.sociologist http://www.linkedin.com/in/marcasmith http://www.slideshare.net/Marc_A_Smith http://www.smrfoundation.org http://www.flickr.com/photos/library_of_congress/3295494976/sizes/o/in/photostream/ http://www.flickr.com/photos/amycgx/3119640267/ Collaboration networks are social networks SNA 101 • Node A – “actor” on which relationships act; 1-mode versus 2-mode networks • Edge B – Relationship connecting nodes; can be directional C • Cohesive Sub-Group – Well-connected group; clique; cluster A B D E • Key Metrics – Centrality (group or individual measure) D • Number of direct connections that individuals have with others in the group (usually look at incoming connections only) E • Measure at the individual node or group level – Cohesion (group measure) • Ease with which a network can connect • Aggregate measure of shortest path between each node pair at network level reflects average distance – Density (group measure) • Robustness of the network • Number of connections that exist in the group out of 100% possible – Betweenness (individual measure) F G • -
Separator Theorems and Turán-Type Results for Planar Intersection Graphs
SEPARATOR THEOREMS AND TURAN-TYPE¶ RESULTS FOR PLANAR INTERSECTION GRAPHS JACOB FOX AND JANOS PACH Abstract. We establish several geometric extensions of the Lipton-Tarjan separator theorem for planar graphs. For instance, we show that any collection C of Jordan curves in the plane with a total of m p 2 crossings has a partition into three parts C = S [ C1 [ C2 such that jSj = O( m); maxfjC1j; jC2jg · 3 jCj; and no element of C1 has a point in common with any element of C2. These results are used to obtain various properties of intersection patterns of geometric objects in the plane. In particular, we prove that if a graph G can be obtained as the intersection graph of n convex sets in the plane and it contains no complete bipartite graph Kt;t as a subgraph, then the number of edges of G cannot exceed ctn, for a suitable constant ct. 1. Introduction Given a collection C = fγ1; : : : ; γng of compact simply connected sets in the plane, their intersection graph G = G(C) is a graph on the vertex set C, where γi and γj (i 6= j) are connected by an edge if and only if γi \ γj 6= ;. For any graph H, a graph G is called H-free if it does not have a subgraph isomorphic to H. Pach and Sharir [13] started investigating the maximum number of edges an H-free intersection graph G(C) on n vertices can have. If H is not bipartite, then the assumption that G is an intersection graph of compact convex sets in the plane does not signi¯cantly e®ect the answer. -
Bellwethers and the Emergence of Trends in Online Communities
Bellwethers and the Emergence of Trends in Online Communities Yasuaki Sakamoto ([email protected]) Elliot Sadlon ([email protected]) Jeffrey V. Nickerson ([email protected]) Center for Decision Technologies Howe School of Technology Management, Stevens Institute of Technology Castle Point on Hudson, Hoboken, NJ 07030 USA Abstract Group-level phenomena, such as trends and congestion, are difficult to predict as behaviors at the group-level typically di- verge from simple aggregates of behaviors at the individual- level. In the present work, we examine the processes by which collective decisions emerge by analyzing how some arti- cles gain vast popularity in a community-based website, Digg. Through statistical analyses and computer simulations of hu- man voting processes under varying social influences, we show that users’ earlier choices have some influence on the later choices of others. Moreover, the present results suggest that there are special individuals who attract followers and guide the development of trends in online social networks. Keywords: Trends, trendsetters, group behavior, social influ- ence, social networks. Figure 1: A snapshot of Digg homepage. Background An individual’s decisions are often influenced by the context the social (Levine, Resnick, & Higgins, 1993) and distributed or the environment in which the decisions are made. For ex- (Hutchins, 1995) nature of learning and thinking in cognitive ample, preferences between two choices can change when a science (Goldstone & Janssen, 2005; Harnad & Dror, 2006). third option is introduced (Tversky, 1972). At the same time, The past work in collective behavior tends to focus on peo- an individual’s actions alter the environments. By modifying ple’s behavior in controlled laboratory experiments (Gureckis their surroundings, humans indirectly communicate to one & Goldstone, 2006), following the tradition of research in in- another and influence one another’s cognition. -
Albert-László Barabási with Emma K
Network Science Class 5: BA model Albert-László Barabási With Emma K. Towlson, Sebastian Ruf, Michael Danziger and Louis Shekhtman www.BarabasiLab.com Section 1 Introduction Section 1 Hubs represent the most striking difference between a random and a scale-free network. Their emergence in many real systems raises several fundamental questions: • Why does the random network model of Erdős and Rényi fail to reproduce the hubs and the power laws observed in many real networks? • Why do so different systems as the WWW or the cell converge to a similar scale-free architecture? Section 2 Growth and preferential attachment BA MODEL: Growth ER model: the number of nodes, N, is fixed (static models) networks expand through the addition of new nodes Barabási & Albert, Science 286, 509 (1999) BA MODEL: Preferential attachment ER model: links are added randomly to the network New nodes prefer to connect to the more connected nodes Barabási & Albert, Science 286, 509 (1999) Network Science: Evolving Network Models Section 2: Growth and Preferential Sttachment The random network model differs from real networks in two important characteristics: Growth: While the random network model assumes that the number of nodes is fixed (time invariant), real networks are the result of a growth process that continuously increases. Preferential Attachment: While nodes in random networks randomly choose their interaction partner, in real networks new nodes prefer to link to the more connected nodes. Barabási & Albert, Science 286, 509 (1999) Network Science: Evolving Network Models Section 3 The Barabási-Albert model Origin of SF networks: Growth and preferential attachment (1) Networks continuously expand by the GROWTH: addition of new nodes add a new node with m links WWW : addition of new documents PREFERENTIAL ATTACHMENT: (2) New nodes prefer to link to highly the probability that a node connects to a node connected nodes.