4
The Definition and Promise of Network Science

In preceding chapters the committee demonstrated the importance of networks to society in general and the Army in particular. It documented that there is interest in research on the properties of networks in any number of civilian and military applications. The committee also established that a pressing national demand exists for “the creation of a new field of investigation called network science to advance knowledge of complex systems and processes that exhibit network behavior,” as expressed in the statement of task. In this chapter it addresses the question of how network science should be defined and positioned.

WHAT IS NETWORK SCIENCE?

The first item in the statement of task (Box 1-2) asks how the new field of investigation called network science envisioned by the committee should be defined. The committee’s research into this seemingly simple question created a surprisingly complex response.

Logically, the notion of network science is straightforward. It is the organized knowledge of networks based on their study using the scientific method. This notion is immediately valuable in that it distinguishes science from technology. Throughout human history technology often evolved far earlier than the scientific knowledge on which it is based. A classic example is the creation of advanced technologies for the production of metal tools and weapons far in advance of the science of metallurgy.

This is the case today for networks. Although the technologies underlying the design, construction, and operation of the global physical communications, information, and distribution networks described earlier are quite advanced, the underlying scientific knowledge has remained rather rudimentary, according to the experts and literature surveyed by the committee. Developing the metallurgy analogy further, the current state of knowledge about physical communication and information networks is similar to the knowledge of metallurgy for weapons and tools in 16th century Europe (Diamond, 1999). Quite sophisticated steel swords and, ultimately, guns were made by entirely empirical processes for creating and forming the steel, without knowing anything about atomic structure, grain boundaries, or the influence of processing on grain boundaries and dislocations. The development of atomic-level metallurgy in the 20th century enabled a quantum leap in the engineering of lightweight, high-strength materials (e.g., for turbine blades and aircraft). However, the weapons created using the empirical technology of the 16th through 19th centuries enabled Europeans to conquer the world during that period, just as modern communications and information technology can and will transform the battlefields of the 21st century. The components of modern communication and information networks are the result of technologies based on fundamental knowledge emanating from physics, chemistry, and materials science. Their assembly into networks, however, is based largely on empirical knowledge rather than on a deep understanding of the principles of network behaviors gained from an underlying science of networks.

In this report the committee examines the state of fundamental knowledge emanating from research on the science of networks rather than the state of empirical knowledge emanating from research on the technologies that go into the construction of physical networks. This is a profound and fundamental distinction that must be appreciated to understand the report. Its flavor may be illustrated by contrasting the concepts of discovery and invention. In a scientific study pursuing new fundamental knowledge, discoveries are made about how the objects of study behave. For example, in the study of the complex three-dimensional network formed by magnetic atoms in solid atomic lattices, the emergent behavior of phase transitions to various ordered states was discovered experimentally and predicted by sophisticated analyses of network models that describe the interactions between the spins on nearby lattice sites (Binney et al., 1992). This is a discovery in the science of networks that illustrates what sorts of network structures and dynamics are required to pre-



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Network Science 4 The Definition and Promise of Network Science In preceding chapters the committee demonstrated the importance of networks to society in general and the Army in particular. It documented that there is interest in research on the properties of networks in any number of civilian and military applications. The committee also established that a pressing national demand exists for “the creation of a new field of investigation called network science to advance knowledge of complex systems and processes that exhibit network behavior,” as expressed in the statement of task. In this chapter it addresses the question of how network science should be defined and positioned. WHAT IS NETWORK SCIENCE? The first item in the statement of task (Box 1-2) asks how the new field of investigation called network science envisioned by the committee should be defined. The committee’s research into this seemingly simple question created a surprisingly complex response. Logically, the notion of network science is straightforward. It is the organized knowledge of networks based on their study using the scientific method. This notion is immediately valuable in that it distinguishes science from technology. Throughout human history technology often evolved far earlier than the scientific knowledge on which it is based. A classic example is the creation of advanced technologies for the production of metal tools and weapons far in advance of the science of metallurgy. This is the case today for networks. Although the technologies underlying the design, construction, and operation of the global physical communications, information, and distribution networks described earlier are quite advanced, the underlying scientific knowledge has remained rather rudimentary, according to the experts and literature surveyed by the committee. Developing the metallurgy analogy further, the current state of knowledge about physical communication and information networks is similar to the knowledge of metallurgy for weapons and tools in 16th century Europe (Diamond, 1999). Quite sophisticated steel swords and, ultimately, guns were made by entirely empirical processes for creating and forming the steel, without knowing anything about atomic structure, grain boundaries, or the influence of processing on grain boundaries and dislocations. The development of atomic-level metallurgy in the 20th century enabled a quantum leap in the engineering of lightweight, high-strength materials (e.g., for turbine blades and aircraft). However, the weapons created using the empirical technology of the 16th through 19th centuries enabled Europeans to conquer the world during that period, just as modern communications and information technology can and will transform the battlefields of the 21st century. The components of modern communication and information networks are the result of technologies based on fundamental knowledge emanating from physics, chemistry, and materials science. Their assembly into networks, however, is based largely on empirical knowledge rather than on a deep understanding of the principles of network behaviors gained from an underlying science of networks. In this report the committee examines the state of fundamental knowledge emanating from research on the science of networks rather than the state of empirical knowledge emanating from research on the technologies that go into the construction of physical networks. This is a profound and fundamental distinction that must be appreciated to understand the report. Its flavor may be illustrated by contrasting the concepts of discovery and invention. In a scientific study pursuing new fundamental knowledge, discoveries are made about how the objects of study behave. For example, in the study of the complex three-dimensional network formed by magnetic atoms in solid atomic lattices, the emergent behavior of phase transitions to various ordered states was discovered experimentally and predicted by sophisticated analyses of network models that describe the interactions between the spins on nearby lattice sites (Binney et al., 1992). This is a discovery in the science of networks that illustrates what sorts of network structures and dynamics are required to pre-

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Network Science dict such behaviors. Contrast this to the invention of the protocol stacks used in the Open Systems Interconnection (OSI) and Transmission Control Protocol/Internet Protocol (TCP/ IP) reference models for the Internet (Tanenbaum, 2003). These models were invented to produce reliable connections between computers under some assumed conditions. They work when these conditions are satisfied but are not necessarily suitable for substantially different network structures like those needed for interplanetary communications (Jackson, 2005). They do not address such issues as whether there exist conditions under which the networks on which they run might exhibit emergent behaviors, i.e., behaviors not predictable from the known behaviors of their components. This report is devoted to an assessment of the current state and future prospects of scientific discoveries about networks rather than of the improvement of the technologies of the components of physical networks or the invention of methodologies for integrating these components into networks to solve specific problems. The fact that network science is logically conceivable does not imply, however, that the concept has been realized in practice. The term “network science” evokes dramatically different images in the minds of workers in different applications domains. The communications engineer envisages the knowledge needed to design a complex communications network like the Internet or the telephone system. The sociologist thinks of networks of influence, like boards of directors or certain social organizations. The business person visualizes the study of informal human networks that enable firms to function, like supply networks and influence networks within large organizations. The physicist thinks of the theory of complex systems, focusing on how order emerges from the apparently random interactions between the nodes through phase transitions or self-organization. The power engineer envisages the knowledge underlying the design and control of the electric power grid. The cell biologist contemplates models of genetic and metabolic networks that enable cell function. And so it goes. The committee addressed this situation by conducting two inquiries. First, it inquired whether there was a body of knowledge widely thought of as being the content of network science that was taught in universities. The results of this inquiry are reported in Chapter 5 and Appendix C. Second, it asked the practitioners of various applications of networks about their notions of network science. The results of this second inquiry are reported in Chapter 6 and Appendix D. What the committee discovered was that practitioners in each major applications area had their own local nomenclatures to describe network models of the phenomena in which they were interested and their own notions of the content of network science. These notions overlap, but are not identical. Finding 4-1. Today there is no encompassing science of networks reflected in the practices and perceptions of practitioners of network research and development. That is, the committee’s research validated the implication in the statement of task that such a “new field of investigation” has yet to be codified. The committee’s point of view is that the operational definition of network science is what the community of researchers who view themselves as working in this field of investigation actually do. Because a coherent community does not exist across the various applications areas, an opportunity exists for the Army to nucleate such a field by its leadership and funding policies. This opportunity is real rather than virtual because a modest consensus exists among network researchers as to what a core “network science” might encompass. The committee developed the substance of this consensus in Chapters 5 and 6. Network science will evolve into whatever its practitioners create. Those two chapters therefore describe the current state of this rapidly evolving area of investigation. Finding 4-2. The notion of a science of networks is evolving, and there is limited understanding of its ultimate scope and content. The communities from which network science is expected to emerge encompass many disciplines and applications areas. Today these communities are characterized by a diversity of nomenclature, models, and opinions about which aspects of the topic are most important. New terms and concepts proliferate. Some are common across many fields—for example, across statistics, economics, sociology, and biology. Others are found in only one or a few subfields—for example, molecular biology, neurology, epidemiology, and ecology, all within biology. Some are given different labels in different fields while meaning essentially the same thing. As documented in Chapter 5, there seems to be a widespread realization that codifying a common nomenclature and body of core knowledge would be useful, but this has not yet occurred. This is why the task statement’s concept of a “new field of investigation called network science” is both sensible and timely. Describing the communities of practice from which the science might emerge does not suffice to provide an operational definition of network science. In addition we must describe its scope and content. Given the rapid evolution of research in this area, this must be done at a high level of abstraction. The details will change significantly over time. The notion of a network is abstracted from the physical, biological, or social realities that are experimentally observed. As discussed in Chapters 5 and 6, a network is described by its structure (e.g., nodes and links), its dynamics (the temporal attributes of nodes and links), and its behaviors (what the network “does” as a result of the interactions among the nodes and links). Thus, a network is always a representation or model of observable reality, not that reality itself. This creates interesting questions about the uniqueness of a specific network representation of a particular phenomenon—for example, the network model of a metabolic

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Network Science process. It is difficult to establish that a successful network model of a social or biological process is unique in the sense that Maxwell’s equations uniquely describe the propagation of electromagnetic waves independent of the details of the associated physical environment. The statement of task asks how a new field of investigation called network science should be defined. Given the evolving notion of a science of networks, any answer to this question will be ephemeral, and the scope and content of network science will evolve as its practitioners develop it. Proposing a formal definition entails two additional risks. First, since the various network application communities perceive this topic in different ways, some of them are likely to criticize, even reject, any definition offered. Second, in light of this possibility, differences of opinion over the definition may become a rationale for discounting the contents of this report. Nevertheless, in the spirit of providing the Army with a framework for thinking about what network science might become, the committee offers the following tentative definition: Finding 4-3. Network science consists of the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena. By focusing on the development of models and properties of the underlying representations, this new area of scientific investigation offers the promise of developing tools, techniques, and models that apply to multiple applications areas. It also offers the happy prospect of simplifying and codifying a variety of nomenclatures and lexicons. Thus, one may reasonably expect that creation of a field called network science will not only provide a body of rigorous results that improve the predictability of the engineering design of complex networks, but also speed up basic research in a variety of applications areas. (The defining characteristics of a network and its behaviors are explored further in Chapter 6.) POSITIONING OF NETWORK SCIENCE Science tells us how the world operates, and technology gives us practical applications of the resulting insights. These make their way into various sectors of society: into the medical tools, procedures, and remedies of our health-care sector, into the products and services of our economy at large, into the texts and classrooms of our educational centers, into the laws and administration of our government, and into the weapons and communications systems of our military. Paths leading to military strength, health-care excellence, a trained labor force and economic vibrancy all follow the flow from science to technology to institutional forms and applications in their plentiful variety. These paths all have beginnings and endings, with specific tasks and characteristics at different points along the way. They begin in gestation, reach an inflection point and grow rapidly, mature when their application is readily understood and widespread, then ultimately age and decline. The quarters of a life cycle are gestation, growth, maturity, and decline. They control not only biological life, but the lives of nations and economies as well (Perez, 2002). We see this in a seed that sprouts, flowers, and dies; in a product that passes through research and development (R&D) into the marketplace and then into every home; and in an Army that pioneers systems that spread throughout the military, then on into society at large, passing from the arcane to ubiquity and, ultimately, to obsolescence. Ultimately, all cycles are surpassed by another cycle—be it of organism, product, or weapons system—that is better adapted to the extant surroundings. In this life cycle context, network science is somewhere near the end of its gestation, poised for takeoff and growth in the decade ahead. When new paradigms first appear, the scientific communities that pertain have little or no social organization. In the growth phase of their cycle, groups of collaborators and “invisible colleges” characteristic of a more mature science develop around their bodies of knowledge. Network science is ready to complete this first phase but is not yet ready to enter its growth stage. The Army can play a crucial role in facilitating the transition now. Indeed, truly surprising results might arise from a systematic study of network science. For example, it is widely held that a revised military paradigm is needed to address evolving threats and opportunities associated with terrorism at home and abroad. These threats arise from network behaviors, specifically the adaptation of social networks to the increasing capabilities of communication and information networks (Arquilla and Ronfeldt, 2001; Berkowitz, 2003). This adaptive phenomenon has been observed over the centuries. Typically, engineered networks designed with one set of social behaviors in mind are, over time, exploited by disruptive elements (e.g., criminals and terrorists) for their own purposes. This is a general historical pattern, examples of which include disruption of commercial naval shipping by pirates in the 18th century, train robberies in the 19th century, airplane hijackings in the 20th century, and terrorism and cybercrime in the 21st century, including the destruction of the World Trade Center on September 11, 2001. Large infrastructure networks evolve over time; society becomes more dependent on their proper functioning; disruptive elements learn to exploit them; and society is faced with challenges, never envisaged initially, to the control and robustness of these networks. Society responds by adapting the network to the disruptive elements, but the adaptations generally are not totally satisfactory. This produces a demand for better knowledge of the design and operation of both the infrastructure networks themselves and the social networks that exploit them. This demand cannot be met by existing knowledge, because the circumstances that create it were not anticipated when the networks were designed and built.

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Network Science Finding 4-4. A gap exists between currently available knowledge about networks and the knowledge required to characterize, design, and operate the complex global physical, information, biological, and social networks on which the well-being of our citizens has come to depend. Closing this gap is an urgent matter, because society has become dependent on the reliable, robust operation of complex global communication, information, transportation, power, and business networks. The disruption or exploitation of these networks by adversarial social networks of terrorists or criminals is a demonstrated threat, making an investment in network science not only strategically sound but also politically urgent. Finding 4-5. Advances in network science can address the threats of greatest importance to the nation’s security. In summary, the committee finds that although there is not universal agreement on what network science is today, there is an emerging consensus on what it can become tomorrow. Moreover, there is a pressing demand for the fundamental knowledge that can be expected to emanate from such a science. Thus, network science is positioned as an emerging new field of investigation at the beginning of its growth curve and of compelling national interest and one that the Army has a unique opportunity to nucleate. In Chapters 5 and 6, the committee turns to an exposition of the results of its research on the content, status, and challenges of this emerging field. Then, in Chapter 7, it articulates how the Army can create value by nucleating the new field and supporting its growth. REFERENCES Arquilla, J., and D. Ronfeldt. 2001. Networks and Netwars: The Future of Terror, Crime, and Militancy. Santa Monica, Calif.: RAND. Berkowitz, B. 2003. The New Face of War: How War Will Be Fought in the 21st Century. New York, N.Y.: Free Press. Binney, J.J., N.J. Dowrick, A.J. Fisher, and M.E.J. Newman. 1992. The Theory of Critical Phenomena. Oxford, England: Clarendon Press. Diamond, J. 1999. Guns, Germs and Steel: The Fates of Human Societies. New York, N.Y.: W.W. Norton. Jackson, J. 2005. The Interplantery Internet. IEEE Spectrum Online. Available at http://www.spectrum.ieee.org/WEBONLY/publicfeature/aug05/0805inte.html. Accessed August 22, 2005. Perez, C. 2002. Technological Revolutions and Financial Capital: The Dynamics of Bubbles and Golden Ages. Cheltenham, England: Edward Elgar Publishers. Tanenbaum, A.S. 2003. Computer Networks, 4th edition. Upper Saddle River, N.J.: Prentice Hall PTR.