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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