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Network Science 5 The Content of Network Science In this chapter, the committee determines topics for inclusion within the boundaries of network science and network science research as a “new field of investigation.” The chapter describes the activities conducted to help define the scope and content of network science and presents the committee’s factual findings. HOW DO WE KNOW? To arrive at a definition of network science and identify the topics that it might encompass, the committee undertook two activities. First, a team of committee members expert in the domains of engineered, physical, biological, and social networks reviewed available academic courses to determine their topical contents. The common elements of the courses were extracted and taken to be a provisional de facto specification of the topics contained in the core science spanning these diverse applications areas. The team’s proposal was then circulated to selected academicians for suggestions and refinement, and the results of this effort are collected in Appendix C. Second, the questionnaire described in Appendix D was circulated to over 1,000 experts in applications areas pertinent to network science asking them for their definitions of the term and their notions of appropriate topical content. The results from the questionnaire, described in Chapter 6 and Appendix D, confirmed the results of the first effort and assisted the committee to elaborate a working definition of network science (Finding 4-3). The results from both efforts further revealed that the term “network science” evoked different mental models in different individuals and communities. What follows is an articulation of the common elements of these mental models. CONTENT As discussed in Chapter 4, network science means different things to different people. It does not exist today as a coherent field of investigation. The committee was charged with assessing whether turning it into a new field with this name would be feasible and useful. One test of the utility of doing so would be to examine the extent to which current research on networks exhibits a core content that cuts across the diverse applications areas. The questionnaire results discussed in Chapter 6 reveal that there are common elements in these diverse applications that can help to create an operational definition of the field pertinent to the committee’s statement of task. Specifically, there seems to be widespread agreement that the common core of network science is the study of complex systems whose behavior and responses are determined by exchanges and interactions between subsystems across a well-defined (possibly dynamic) set of pathways. The central point is that the behavior of a network is determined both by the pathways (structure) and by the exchanges and interactions (dynamics). Moreover the structure itself may be (and usually is) dynamic. This is a flexible definition that allows flexible interpretation in the various applications domains. It is elaborated upon and extended in Chapter 6. A central outcome of the committee’s work is the realization that network ideas span an enormous range of disciplines and applications domains. As might be expected, researchers in each domain have their own terminologies and lexicons, so communication among them is not always straightforward. There is a growing notion that these dialects mask an underlying commonality, but the nature of this commonality remains fluid. Finding 5-1. Network science is an emerging discipline whose boundaries are evolving. For network science to be regarded as a science, it must encompass core principles that can be taught to students. These core principles, generally embedded in quantitative models, should enable predictions of network behaviors given the structure and dynamics of the network as inputs.
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Network Science These predictions must be testable experimentally so they can either be verified or proven false. Moreover, the core principles and their associated models and tests will need to be captured in a core curriculum that can be communicated to students. The committee found broad agreement among experts in diverse applications domains on a set of core topics that would need to be mastered to pursue a discipline labeled as “network science.” Finding 5-2. There is broad agreement among experts on topics necessary for inclusion as the core content of network science. The specific topics included in the core content are described in Appendix C. The central notion is that a network is described by its structure and dynamics, which combine to provide a complete specification of its properties (including functions and behaviors). The structure of a network is specified by indicating which nodes are linked to which other nodes and whether the links are unidirectional or bidirectional. From this information a number of figures of merit characterizing the structure of the network can be determined. Textbooks and major review articles have been written on this topic (Albert and Barabási, 2002; Dorogovtsev and Mendes, 2003; Newman, 2003; Watts, 2004). The calculation of these figures of merit for various classes of structural models for networks is a staple of courses on networks and an essential core ingredient of network science. The specification of the dynamics of a network is less straightforward because the dynamics tend to be rather different in the various applications areas. One example is the analysis of phase transitions in physical systems—for example, magnetic atoms in solids. Here the dynamics are specified by the interactions between the spins of the magnetic atoms, which typically vary as a function of the distance between them (Binney et al., 1992). In chemistry and biology, network models are used to describe sequences of chemical reactions. The nodes are typically the reactants and products, with the links being their chemical reactions. The dynamics can be specified by logical models, by rate equations, or by stochastic models of individual reactions (Bower and Bolouri, 2001). In sociology, the nodes are typically people and the links are their interactions. The dynamics are often specified by state models in which the state of one person depends on the states of the other persons with whom she/he interacts as well as on some internal predisposition, often specified statistically (Watts, 2004). Thus, the model dynamics that are introduced in a core course typically depend on the classes of applications that the instructor has in mind. The essence of network science is making testable predictions about the properties of a network once its structure and dynamics have been specified. A body of knowledge about the standard models and tools for analyzing networks has accumulated over time, as indicated in Appendix C. Because these models and tools constitute knowledge that is often reused in multiple applications areas, they are the remaining elements in the core content of network science. The core content of network science is basic science, currently consisting of simplified models and of techniques that are appropriate for the analysis of small networks that exhibit low topological complexity in the terminology of Table 2-2. The analysis of network structure is more advanced than that of network dynamics. If adequate structural data are available, structure analysis techniques can be applied to larger and more complex networks using available computer tools. The outputs of model analyses in the core content are insight and qualitative understanding, not engineering design. The specification of architecture and the design of the physical type networks described in Tables 2-1 and 2-2 are the province of engineering applications domains. The structure, dynamics, and function of the biological and social type networks mentioned in the tables are the subjects of basic research. The application of electromagnetic theory to the design of the power grid affords a useful analogy. Even a graduate physics course in electromagnetism is of little direct use in designing the power grids noted in Tables 2-1 and 2-2. The material in the core content of network science is analogous to that taught in graduate and undergraduate courses in electromagnetism. Finding 5-3. Research contributing to the core content of network science is basic research (6.1) in the DOD classification scheme. When the demands on network science imposed by its desired applications are compared with the current state of the knowledge about the science described in Appendix C, a yawning gap appears. The applications require validated theories that allow predicting the properties of global-scale networks under stress conditions. Current knowledge consists of simplified models and tools for analyzing relatively small and simple networks. It seems clear to the committee that substantial development of the core content of network science is required for it to become adequate for its intended applications. Finding 5-4. Significant investment in the development of the core content of network science is required in order to create adequate knowledge to meet current demands for the characterization, analysis, design, and operation of complex networks. The networks described in Chapter 2 tend to be both large and complex. They are large if they have many interacting components, typically millions or more for physical networks like the Internet, regional power grids, or transistors on a chip. They are complex if their components exhibit
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Network Science known behaviors, but our knowledge of these behaviors does not suffice to predict the behaviors of the network as a whole (Boccara, 2004). Such complex networks are said to exhibit emergent behavior if the behaviors of their components lead to unanticipated—that is, “emergent”—behavior of the network as a whole in the absence of a centralized controller that creates this behavior by design. As an example, the network of transistors on a computer chip is not normally regarded as exhibiting emergent behavior, whereas an ant colony or the World Wide Web is (Boccara, 2004). It seems to be widely accepted that investment in basic research will be required to describe the behaviors of social and biological networks. A similar call for investment in basic research might appear counterintuitive for technologically advanced physical networks like the Internet or regional power grids. A few moments of reflection reveals, however, that these physical networks, too, exhibit emergent behaviors. The Internet is robust against expected noises but fragile against unexpected ones, like computer viruses (Doyle et al., 2005). Regional power grids fail infrequently but inevitably, under circumstances not anticipated by grid designers and not adequately dealt with by grid power control systems (IEEE Spectrum, 2004). Contrary to the efforts and hopes of the implementers of advanced technologies, the behaviors of complex physical networks are not yet completely predictable. Moreover, spending to improve the technologies in their components will not remedy this situation. Just like the development of radar awaited the basic science of electromagnetism and that of nuclear weapons awaited the discovery of nuclear fission, the ability to control the complex networks in our lives awaits as yet unforeseen discoveries in the science of networks. Because committees are notoriously inept at developing curricula or specifying the research content of a science discipline, this committee makes no attempt to do either. It offers the analysis given in Appendix C and discussed above as a test of the proposition that network science be regarded as a coherent area of investigation worthy of investment by the Army. The committee believes that network science fully passes this test. REFERENCES Albert, R., and A.L. Barabási. 2002. Statistical mechanics of complex networks. Reviews of Modern Physics 74(1): 47–97. Binney, J.J., N.J. Dowrick, A.J. Fisher, and M.E.J. Newman. 1992. The Theory of Critical Phenomena. Oxford, England: Clarendon Press. Boccara, N. 2004. Modeling Complex Systems. New York, N.Y.: Springer. Bower, J.M., and H. Bolouri. 2001. Computational Modeling of Genetic and Biochemical Networks. Cambridge, Mass.: MIT Press. Dorogovtsev, S.N., and J.F.F. Mendes. 2003. Evolution of Networks: From Biological Nets to the Internet and WWW. Oxford, England: Oxford University Press. Doyle, J.C., D. Alderson, L. Lun, S. Low, M. Roughan, S. Schalunov, R. Tanaka, and W. Willinger. 2005. The “Robust yet Fragile” Nature of the Internet. Proceedings of the National Academy of Sciences (PNAS) 102(41): 14497–14502. IEEE Spectrum. 2004. The Unruly Power Grid. IEEE Spectrum August 2004: 22–27. Newman, M.E.J. 2003. The structure and function of complex networks. SIAM Review 45(2): 167–256. Watts, D. 2004. The “new” science of networks. Annual Review of Sociology 30(1): 243–270.
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