Multidimensional Network Analysis
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Opinion-Based Centrality in Multiplex Networks: a Convex Optimization Approach
Opinion-Based Centrality in Multiplex Networks: A Convex Optimization Approach Alexandre Reiffers-Masson and Vincent Labatut Laboratoire Informatique d'Avignon (LIA) EA 4128 Universit´ed'Avignon, France June 12, 2017 Abstract Most people simultaneously belong to several distinct social networks, in which their relations can be different. They have opinions about certain topics, which they share and spread on these networks, and are influenced by the opinions of other persons. In this paper, we build upon this observation to propose a new nodal centrality measure for multiplex networks. Our measure, called Opinion centrality, is based on a stochastic model representing opinion propagation dynamics in such a network. We formulate an optimization problem consisting in maximizing the opinion of the whole network when controlling an external influence able to affect each node individually. We find a mathematical closed form of this problem, and use its solution to derive our centrality measure. According to the opinion centrality, the more a node is worth investing external influence, and the more it is central. We perform an empirical study of the proposed centrality over a toy network, as well as a collection of real-world networks. Our measure is generally negatively correlated with existing multiplex centrality measures, and highlights different types of nodes, accordingly to its definition. Cite as: A. Reiffers-Masson & V. Labatut. Opinion-based Centrality in Multiplex Networks. Network Science, 5(2):213-234, 2017. Doi: 10.1017/nws.2017.7 1 Introduction In our ultra-connected world, many people simultaneously belong to several distinct social networks, in which their relations can be different. -
Directed Graphs Definition: an Directed Graph (Or Digraph) G = (V, E) Consists of a Nonempty Set V of Vertices (Or Nodes) and a Set E of Directed Edges (Or Arcs)
Chapter 10 Chapter Summary Graphs and Graph Models Graph Terminology and Special Types of Graphs Representing Graphs and Graph Isomorphism Connectivity Euler and Hamiltonian Graphs Shortest-Path Problems (not currently included in overheads) Planar Graphs (not currently included in overheads) Graph Coloring (not currently included in overheads) Section 10.1 Section Summary Introduction to Graphs Graph Taxonomy Graph Models Graphs Definition: A graph G = (V, E) consists of a nonempty set V of vertices (or nodes) and a set E of edges. Each edge has either one or two vertices associated with it, called its endpoints. An edge is said to connect its endpoints. Example: a b This is a graph with four vertices and five edges. d c Remarks: The graphs we study here are unrelated to graphs of functions studied in Chapter 2. We have a lot of freedom when we draw a picture of a graph. All that matters is the connections made by the edges, not the particular geometry depicted. For example, the lengths of edges, whether edges cross, how vertices are depicted, and so on, do not matter A graph with an infinite vertex set is called an infinite graph. A graph with a finite vertex set is called a finite graph. We (following the text) restrict our attention to finite graphs. Some Terminology In a simple graph each edge connects two different vertices and no two edges connect the same pair of vertices. Multigraphs may have multiple edges connecting the same two vertices. When m different edges connect the vertices u and v, we say that {u,v} is an edge of multiplicity m. -
Networkx: Network Analysis with Python
NetworkX: Network Analysis with Python Salvatore Scellato Full tutorial presented at the XXX SunBelt Conference “NetworkX introduction: Hacking social networks using the Python programming language” by Aric Hagberg & Drew Conway Outline 1. Introduction to NetworkX 2. Getting started with Python and NetworkX 3. Basic network analysis 4. Writing your own code 5. You are ready for your project! 1. Introduction to NetworkX. Introduction to NetworkX - network analysis Vast amounts of network data are being generated and collected • Sociology: web pages, mobile phones, social networks • Technology: Internet routers, vehicular flows, power grids How can we analyze this networks? Introduction to NetworkX - Python awesomeness Introduction to NetworkX “Python package for the creation, manipulation and study of the structure, dynamics and functions of complex networks.” • Data structures for representing many types of networks, or graphs • Nodes can be any (hashable) Python object, edges can contain arbitrary data • Flexibility ideal for representing networks found in many different fields • Easy to install on multiple platforms • Online up-to-date documentation • First public release in April 2005 Introduction to NetworkX - design requirements • Tool to study the structure and dynamics of social, biological, and infrastructure networks • Ease-of-use and rapid development in a collaborative, multidisciplinary environment • Easy to learn, easy to teach • Open-source tool base that can easily grow in a multidisciplinary environment with non-expert users -
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. -
Adjacency and Incidence Matrices
Adjacency and Incidence Matrices 1 / 10 The Incidence Matrix of a Graph Definition Let G = (V ; E) be a graph where V = f1; 2;:::; ng and E = fe1; e2;:::; emg. The incidence matrix of G is an n × m matrix B = (bik ), where each row corresponds to a vertex and each column corresponds to an edge such that if ek is an edge between i and j, then all elements of column k are 0 except bik = bjk = 1. 1 2 e 21 1 13 f 61 0 07 3 B = 6 7 g 40 1 05 4 0 0 1 2 / 10 The First Theorem of Graph Theory Theorem If G is a multigraph with no loops and m edges, the sum of the degrees of all the vertices of G is 2m. Corollary The number of odd vertices in a loopless multigraph is even. 3 / 10 Linear Algebra and Incidence Matrices of Graphs Recall that the rank of a matrix is the dimension of its row space. Proposition Let G be a connected graph with n vertices and let B be the incidence matrix of G. Then the rank of B is n − 1 if G is bipartite and n otherwise. Example 1 2 e 21 1 13 f 61 0 07 3 B = 6 7 g 40 1 05 4 0 0 1 4 / 10 Linear Algebra and Incidence Matrices of Graphs Recall that the rank of a matrix is the dimension of its row space. Proposition Let G be a connected graph with n vertices and let B be the incidence matrix of G. -
Measuring Homophily
Measuring Homophily Matteo Cristani, Diana Fogoroasi, and Claudio Tomazzoli University of Verona fmatteo.cristani, diana.fogoroasi.studenti, [email protected] Abstract. Social Network Analysis is employed widely as a means to compute the probability that a given message flows through a social net- work. This approach is mainly grounded upon the correct usage of three basic graph- theoretic measures: degree centrality, closeness centrality and betweeness centrality. We show that, in general, those indices are not adapt to foresee the flow of a given message, that depends upon indices based on the sharing of interests and the trust about depth in knowledge of a topic. We provide new definitions for measures that over- come the drawbacks of general indices discussed above, using Semantic Social Network Analysis, and show experimental results that show that with these measures we have a different understanding of a social network compared to standard measures. 1 Introduction Social Networks are considered, on the current panorama of web applications, as the principal virtual space for online communication. Therefore, it is of strong relevance for practical applications to understand how strong a member of the network is with respect to the others. Traditionally, sociological investigations have dealt with problems of defining properties of the users that can value their relevance (sometimes their impor- tance, that can be considered different, the first denoting the ability to emerge, and the second the relevance perceived by the others). Scholars have developed several measures and studied how to compute them in different types of graphs, used as models for social networks. This field of research has been named Social Network Analysis. -
Breakdown of Interdependent Directed Networks Xueming Liu, ∗ † H
i i \"SI Appendix"" | 2015/12/23 | 9:13 | page 1 | #1 i i Supporting Information: Breakdown of interdependent directed networks Xueming Liu, ∗ y H. Eugene Stanley y and Jianxi Gao z ∗Key Laboratory of Image Information Processing and Intelligent Control, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China,yCenter for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, and zCenter for Complex Network Research and Department of Physics, Northeastern University, Boston, MA 02115 Submitted to Proceedings of the National Academy of Sciences of the United States of America I. Notions related to interdependent networks Multiplex networks. The agents (nodes) participate in ev- Both natural and engineered complex systems are not isolated ery layer of the network simultaneously. The connections but interdependent and interconnected. Such diverse infras- among these agents in different layers represent different tructures as water supply systems, transportation networks, relationships [14, 15, 28, 29, 13, 30, 31]. For example, a fuel delivery systems, and power stations are coupled together user of online social networks can subscribe to two or more [1]. To study the interdependence between networks, Buldyrev networks and build social relationships with other users on et al. [2] developed an analytic framework based on the gener- a range of social platforms (e.g., LinkedIn for a network of ating function formalism [3, 4] and discovered that the interde- professional contacts or Facebook for a network of friends) pendence between networks sharply increases system vulner- [11, 14]. ability, because node failures in one network can lead to the Temporal 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 -
What Metrics Really Mean, a Question of Causality and Construction in Leveraging Social Media Audiences Into Business Results: Cases from the UK Film Industry
. Volume 10, Issue 2 November 2013 What metrics really mean, a question of causality and construction in leveraging social media audiences into business results: Cases from the UK film industry Michael Franklin, University of St Andrews, UK Summary: Digital distribution and sustained audience engagement potentially offer filmmakers new business models for responding to decreasing revenues from DVD and TV rights. Key to campaigns that aim at enrolling audiences, mitigating demand uncertainty and improving revenues, is the management of digital media metrics. This process crucially involves the interpretation of figures where a causal gap exists between some digital activity and a market transaction. This paper charts the conceptual framing methods and calculations of value necessary to manipulating and utilising the audience in a new way. The invisible aspects and mediating role of contemporary creative industries audiences is presented through empirical case study evidence from two UK feature films. Practitioners’ understanding of digital engagement metrics is shown to be a social construction involving the agency of material artefacts as powerful elements of networks that include both market entities and audiences. Keywords: Film Business; Social Media; Market Device; Valuation; Digital Engagement Introduction The affordances of digital technology for audience engagement and more direct, or dis- intermediated distribution, prompt a reappraisal of the role of audiences in the film industry. Through digital tools, most significantly through social media, audiences are made material. Audiences are interacted with, engaged, marketed to, and financially exploited often visible all their social network connections, but they are also aggregated, manipulated and exert an agency that is much less visible and plays out off-screen. -
Modeling Customer Preferences Using Multidimensional Network Analysis in Engineering Design
Modeling customer preferences using multidimensional network analysis in engineering design Mingxian Wang1, Wei Chen1, Yun Huang2, Noshir S. Contractor2 and Yan Fu3 1 Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA 2 Science of Networks in Communities, Northwestern University, Evanston, IL 60208, USA 3 Global Data Insight and Analytics, Ford Motor Company, Dearborn, MI 48121, USA Abstract Motivated by overcoming the existing utility-based choice modeling approaches, we present a novel conceptual framework of multidimensional network analysis (MNA) for modeling customer preferences in supporting design decisions. In the proposed multidimensional customer–product network (MCPN), customer–product interactions are viewed as a socio-technical system where separate entities of `customers' and `products' are simultaneously modeled as two layers of a network, and multiple types of relations, such as consideration and purchase, product associations, and customer social interactions, are considered. We first introduce a unidimensional network where aggregated customer preferences and product similarities are analyzed to inform designers about the implied product competitions and market segments. We then extend the network to a multidimensional structure where customer social interactions are introduced for evaluating social influence on heterogeneous product preferences. Beyond the traditional descriptive analysis used in network analysis, we employ the exponential random graph model (ERGM) as a unified statistical -
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. -
Powerdesigner 16.6 Data Modeling
SAP® PowerDesigner® Document Version: 16.6 – 2016-02-22 Data Modeling Content 1 Building Data Models ...........................................................8 1.1 Getting Started with Data Modeling...................................................8 Conceptual Data Models........................................................8 Logical Data Models...........................................................9 Physical Data Models..........................................................9 Creating a Data Model.........................................................10 Customizing your Modeling Environment........................................... 15 1.2 Conceptual and Logical Diagrams...................................................26 Supported CDM/LDM Notations.................................................27 Conceptual Diagrams.........................................................31 Logical Diagrams............................................................43 Data Items (CDM)............................................................47 Entities (CDM/LDM)..........................................................49 Attributes (CDM/LDM)........................................................55 Identifiers (CDM/LDM)........................................................58 Relationships (CDM/LDM)..................................................... 59 Associations and Association Links (CDM)..........................................70 Inheritances (CDM/LDM)......................................................77 1.3 Physical Diagrams..............................................................82