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Social Networks Animating the development of Social networks over time using a dynamic extension of multidimensional scaling Animating the development of Social networks over time using a dynamic extension of multidimensional scaling Loet Leydesdorff, Thomas Schank, Andrea Scharnhorst, and Wouter de Nooy Loet Leydesdorff (Ph. D. Thomas Schank is teacher Andrea Scharnhorst is se- Wouter de Nooy, with a Sociology, M. A. Philosophy, and research assistant at the nior research fellow at the background in the sociology and M. Sc. Biochemistry) Universität Karlsruhe, Faculty Virtual Knowledge Studio, a of art and culture, is associate reads Science and Techno- of Informatics. Formerly, he research programme of the professor for research methods logy Dynamics at the Ams- was a teacher and research Royal Netherlands Academy at the Amsterdam School of terdam School of Communi- assistant at the Universität of Arts and Sciences in Ams- Communication Research (AS- cations Research (ASCoR) of Konstanz, did a predoc cour- terdam, where she leads a co- CoR). He specializes in social the University of Amsterdam. se on combinatorics, geome- llaboratory on modeling and network analysis and applica- He is visiting professor of the try, and computation at the simulation in the humanities tions of network analysis to the Institute of Scientific and Te- ETH Zürich. His recent works and social sciences. Her work fields of literature, the visual chnical Information of China deal with network statistics, focuses on the use of mathe- arts, music and arts policy. His (ISTIC) in Beijing, honorary relationships between auto- matical models (in particular international publications have fellow of the Science and nomous systems, approxi- models of self-organization, appeared in Poetics and Social Technology Policy Research mating clustering coefficients evolution and complex syste- Networks. He is one of the au- Unit (SPRU) of the Universi- and transitivity, and drawing ms) as heuristic tools. She has thors of a handbook on social ty of Sussex, and the Virtual graphs on two and three li- edited a book (together with network analysis (Exploratory Knowledge Studio of the Ne- nes. Andreas Pyka), Innovation social network analysis using therlands Royal Academy of networks – New approaches Pajek, Cambridge University Arts and Sciences. in modeling and analyzing. Press, 2005). Abstract: The animation of network visualizations poses technical and theoretical challenges. Rather stable patterns are required before the mental map enables a user to make inferences over time. In order to enhance stability, we developed an extension of stress minimization with developments over time. This dynamic layouter is no longer based on linear interpo- lation between independent static visualizations, but change over time is used as a parameter in the optimization. Because of our focus on structural change versus stability the attention is shifted from the relational graph to the latent eigenvec- tors of matrices. The approach is illustrated with animations for the journal citation environments of Social networks, the (co)author networks in the carrying community of this journal, and the topical development using relations among its title words. Our results are also compared with animations based on PajekToSVGAnim and SoNIA. Keywords: Animation, Network, Network visualization, Dynamic, Stress, Structure, Evolution. Título: Animación de la evolución de la revista Social networks en el tiempo utilizando una ex- tensión dinámica del escalado multidimensional. Resumen: La animación de la visualización de una red plantea desafíos técnicos y teóricos. Se necesitan patrones es- tables para que los usuarios puedan hacer inferencias a través del tiempo. Con el fin de mejorar la estabilidad, hemos desarrollado una extensión de la mínimización del estrés en diagramas que evolucionan a lo largo del tiempo. Este visua- lizador dinámico no se basa en la interpolación lineal entre visualizaciones estáticas independientes, sino que el cambio con el tiempo se utiliza como parámetro en la optimización. Debido a nuestro enfoque cambio estructural versus esta- bilidad, hemos desplazado nuestra atención del grafo relacional a los vectores-eigen latentes de matrices. El método se ilustra con animaciones para el entorno de citas de la revista Social networks, las redes de (co-)autores en la comunidad de dicha revista, y la evolución de temas usando relaciones entre palabras de los títulos. Nuestros resultados se comparan con animaciones basadas en PajekToSVGAnim y SoNIA. Article received on 28-09-08 Acepted on 10-10-08 El profesional de la información, v.17, n. 6, noviembre-diciembre 2008 611 Loet Leydesdorff, Thomas Schank, Andrea Scharnhorst, and Wouter de Nooy Palabras clave: Animación, Red, Dinámico, Estrés, Estructura, Visualización de redes, Evolución. Leydesdorff, Loet; Schank, Thomas; Scharnhorst, Andrea; De Nooy, Wouter D. “Animating the development of Social networks over time using a dynamic extension of multidimensional scaling”. En: El profesional de la información, 2008, noviembre-diciembre, v. 17, n. 6, pp. 611-626. DOI: 10.3145/epi.2008.nov.04 Introduction In this study we take an approach different from the interpolation between independent snapshots at differ- When one extends the visualization of networks ent moments in time. We submit a dynamic extension at each moment in time to the animation of these net- of social network analysis based on stress minimiza- works over time, one encounters a number of technical tion and multidimensional scaling (MDS). Stress can and theoretical problems. The technical ones involve be minimized both at each instant in time and over time the stability of the representation because the human (Baur & Schank, 2008). This algorithmic approach to mind needs to be able to entertain a mental map on the the problem of relating static and dynamic represen- basis of the animation (Misue et al., 1995; Moody et tations was recently implemented in Visone, another al., 2005; Bender-deMoll & McFarland, 2006). The publicly available program for the visualization of so- pattern in the representation has to be stabilized while cial network data. A version of this program with the computer layouts can be mapped, rotated, and sized in- dynamic extension is available online at dependently from one instant to another, using criteria like stress-minimization. The consequent series may be http://www.leydesdorff.net/visone/index.htm distorted or discontinuous to such an extent that one The potential of our approach is illustrated below would no longer be able to draw a mental map or to with animations of: (1) the position of the journal So- infer hypotheses about network growth or structural cial networks among other journals in its citation impact changes from the resulting animations. environment (1994-2006), (2) the development of the More fundamentally, the adjacency matrix of a net- co-author networks in Social networks during the pe- work contains only relational information, not coordi- riod 1988-2007, (3) the topical network in terms of co- nates of the nodes in a metric space. In a static represen- occurrences of title words, and (4) the knowledge base tation of a network, positions can be deduced from the of the publications in Social networks in terms of their network of relations. In a dynamic animation, however, aggregate references to other journals. Furthermore, the the researcher may precisely be interested in changes in pros and cons of using this new algorithm for the anima- positions of nodes. This would require relative stability tion are discussed in relation to PajekToSVGAnim.exe in positioning the nodes (and not the links). Boerner et and SoNIA as two (non-commercial) alternatives. al. (2005), for example, solved this problem by using the last map in a time series to fix the positions of the Theoretical and methodological nodes, and backtracked from this map to its evolution considerations over time by erasing nodes and links from the perspec- When two or more visualizations are generated for tive of hindsight, while keeping the positions constant. different moments in time, one is intuitively inclined to The visualization program Pajek (De Nooy et al., attribute the observable change to changes in the sys- 2005)1 allows for a strategy in which one first generates tem under study. However, one should be aware that a configuration using the aggregate of networks over the positions of nodes and links in the visualization of time as a baseline. Given this initial layout, one can then a network are due to algorithms which optimize the use the positions at each time t as a starting point for the visualization using different criteria for the layout, for optimization at time t + 1. The sequence thus generated example, in order to avoid the unnecessary crossing of can be saved and used as input to PajekToSVGAnim. edges. Any map remains a projection in two dimen- exe2. This program generates an SVG-animation that sions of a multi-dimensional object. Thus, changes in can be brought online. Using their program Social Net- the visualization over time can be attributed to develop- works Image Animator (SoNIA)3, Moody et al. (2005) ments in the system to be visualized or differences in define time windows that span sets of relational events. the optimizations and/or the angle of the projection. The time windows (“bins”) can be overlapping or not. If one considers the relationships as variables de- In these animations the nodes move as functions of re- veloping over time and in relation to one another, one lationships (Bender-deMoll et al., 2006). The anima- would have to consider the partial differential equations tions of SoNIA can be exported as QuickTime movies. for all these variables. This would lead to an analyti- 612 El profesional de la información, v.17, n. 6, noviembre-diciembre 2008 Animating the development of Social networks over time using a dynamic extension of multidimensional scaling cally almost never solvable problem. At issue is that a distributions of relations. In this study, we shall reflex- hidden variable may cause dependency relations among ively use both topologies.
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