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 4.1 Node and Edge Properties .................................................................................................................11 4.2 Local Structure...................................................................................................................................12 4.3 Statistical Properties ..........................................................................................................................16 4.4 Network Types...................................................................................................................................18 4.5 Discussion and Exemplification ........................................................................................................21 5. Network Modeling ................................................................................................................................23 5.1 Modeling Static Networks .................................................................................................................23 5.2 Modeling Evolving Networks............................................................................................................27 5.3 Discussion..........................................................................................................................................32 5.4 Model Validation...............................................................................................................................34 6. Modeling Dynamics on Networks........................................................................................................34 7. Network Visualization ..........................................................................................................................41 7.1 Visualization Design Basics ..............................................................................................................42 7.2 Matrix Visualization ..........................................................................................................................44 7.3 Tree Layout........................................................................................................................................45 7.4 Graph Layout.....................................................................................................................................46 7.5 Visualization of Dynamics ................................................................................................................48 7.6 Interaction and Distortion Techniques...............................................................................................50 8. Discussion and Outlook ........................................................................................................................50 Acknowledgments .....................................................................................................................................51 Endnotes ....................................................................................................................................................52 References..................................................................................................................................................52 1 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. 1. Introduction This chapter reviews the highly interdisciplinary field of network science, a science concerned with the study of networks, be they biological, technological, or scholarly networks. It contrasts, compares, and integrates techniques and algorithms developed in disciplines as diverse as mathematics, statistics, physics, social network analysis, information science, and computer science. A coherent theoretical framework including static and dynamical modeling approaches is provided along with discussion of non- equilibrium techniques recently introduced for the modeling of growing networks. The chapter also provides a practical framework by reviewing major processes involved in the study of networks such as network sampling, measurement, modeling, validation and visualization. For each of these processes, we explain and exemplify commonly used approaches. Aiming at a gentle yet formally correct introduction of network science theory, we explain terminology and formalisms in great detail. Although the theories come from a mathematical, formulae laden world, they are highly relevant for the effective design of technological networks, scholarly networks, communication networks, and so on. We conclude with a discussion of promising avenues for future research. At any moment in time, we are driven by and are an integral part of many interconnected, dynamically changing networks1. Our neurons fire, cells are signaling to each other, our organs work in concert. The attack of a cancer cell might have an impact on all of these networks and it also impacts our social and behavioral networks if we become conscious of the attack. Our species has evolved as part of diverse ecological, biological, social, and other networks over thousands of years. As part of a complex food web, we learned how to find prey and to avoid predators. We have created advanced socio-technical environments in the shape of cities, water and power systems, street and airline systems. In 1969, researchers started to interlink computers leading to the largest and most widely used networked infrastructure in existence: the Internet. The Internet facilitated the emergence of the World-Wide Web, a virtual network that interconnects billions of Web pages, datasets, services and human users. Thanks to the digitization of books, papers, patents, grants, court cases, news reports and other material, along with the explosion of Wikipedia entries, e-mails, blogs, and such, we now have a digital copy of a major part of humanity’s knowledge and evolution. Yet, although the amount of knowledge produced per day is growing at an accelerating rate, our main means of accessing mankind’s knowledge is search engines that retrieve matching entities and facilitate local search based on connections, for example, references or Web links. But, it is not only factual knowledge that matters. The more global the problems we need to master as a species, the more we need to identify and understand major connections, trends, and patterns in data, information and knowledge. We need to be able to measure, model, manage, and understand the structure and function of large, networked physical and information systems. Network science is an emerging, highly interdisciplinary research area that aims to develop theoretical and practical approaches and techniques to increase our understanding of natural and man made networks. The study of networks has a long tradition in graph theory and discrete mathematics (Bollobas, 1998; Brandes & Erlebach, 2005), sociology (Carrington, Scott, & Wasserman, 2004; Wasserman & Faust, 1994), communication research (Monge & Contractor, 2003), bibliometrics/scientometrics (Börner, Chen, & Boyack, 2003; Cronin & Atkins 2000), Webometrics/cybermetrics (Thelwall, 2004), biology (Barabási & Oltvai, 2004; Hodgman 2000), and more recently physics (Barabási, 2002; Buchanan, 2002; Dorogovstev & Mendes, 2003; Pastor-Satorras & Vespignani, 2004; Watts, 1999). Consequently, there is impressive variety in the work styles, approaches and research interests among network scientists. Some specialize in the detailed analysis of a certain type of network, for example, friendship networks. Others focus on the search for common laws that might influence the structure and dynamics of networks across application domains. Some scientists apply existing network measurement, modeling and visualization algorithms to new datasets.