Sunday, December 3, 2006

A New Frontier in Theoretical Physics with applications to Biological, Social and Physical Systems: National Academy Report on Network Science (Chaired by Charlie Duke)



Charles B. Duke, Professor of Physics at the University of Rochester, and member of the National Academy of Sciences and National Academy of Engineering chaired the Committee on Network Science of the National Research Council and of the Board on Army Science and Technology ( BAST ). The following is a summary of the report (full text at

Network Science: An Emerging Frontier in Theoretical Physics (11/17/06)

C. B. Duke , )


Networks are ubiquitous in human life. Biological networks control our bodies and our ecosystem. Social networks control our education, work life, and government. Physical networks control our communications, travel, electric power, and water. A new National Research Council report on Network Science documents the profound impact of networks in our daily lives and indicates the content and importance of a science of networks that enables reliable predictions of their behaviors. This is a major emerging frontier of immense interest to physicists, especially those studying complex systems.

The opening days 21st century ushered in the era of connectedness. Today the entire world is connected via the Internet: Literally becoming a global village (see ref 1). We are far more connected than we realize.

A: Modern research in biology has revealed that our bodies operate via complex biological networks that control the operations of our cells, the expression of our genes, our metabolism, the flow of our blood, the working of our mind, and our entire central nervous system (see ref 2).

B: We are all connected to each other by social networks (see ref 3) like schools, churches, social clubs, professional societies, businesses and governmental entities, some of which are rapidly morphing into fundamentally new ways in which humans communicate with each other (see ref 4).

C: Physical networks are well known to us in everyday life: The electric power grid that provides electricity for our homes and businesses, our water and sewer systems, the road and highway network, the rail and airline networks, the telephone network, as well as the physical layer of the internet. These all connect us to each other. Because of the enormous importance of networks to our national and personal well being, the National Research Council (NRC) commissioned a study of Network Science, chaired by Charles Duke of the Physics Department, of how much is really known about the fundamental principles underlying their design and operation. Chapter two in the report on this study (see ref 5) is devoted to cataloging and characterizing the many networks that govern our everyday life.

Physicists are perhaps most familiar with the study of networks as a subset of that of complex systems. Problems that involve the collective behavior of humans or cells or the elements of a cell are in that they involve many feedback loops, often produce counterintuitive behaviors, and most particularly exhibit behaviors that cannot be predicted from those of their components (see ref 5,6). The defining feature of a complex system is that it exhibits "emergent" collective behavior resulting from the interactions among its constituent components that cannot be predicted from the attributes of these components alone (see ref 6).

Condensed matter physicists are quite familiar with such systems. They result in phase transitions to collective states in systems as diverse as superfluids, superconductors, and all sorts of interacting spin systems resulting in collective magnetic behaviors. A key question for network science is how do the collective states (emergent behaviors) depend on the connectivity of the network. This question has been thoroughly studied in magnetic spin systems for which it has long been recognized that the details of the phase diagram depend on the dimensionality of the system, the symmetries of the spin-spin interactions, and the range of these interactions (seee ref 7).

In addition, physicists have recently become interested in applying statistical mechanics techniques to characterize the structure of networks (see ref 6, 8, 9). Considerable progress has been made along these lines. The study of the relation between structure and the resulting dynamics (behaviors) of networks remains, however, in its infancy (see ref 5). This is a current frontier in theoretical physics: One of enormous practical as well as intellectual interest.

Perhaps the most important finding of the NRC study of Network Science is that fundament knowledge about networks is primitive (see ref 5).

Empirical technological and engineering knowledge about the design and operation of physical networks like computer networks (e.g., the Internet), communications networks, the power grid, and water and sewage networks is quite advanced. Nevertheless, these networks exhibit unexpected failure modes and behaviors under stress that were not anticipated by their designers. Social and biological networks are barely characterized, much less described by models that can predict their behaviors.

The study committee emerged from their labors amazed at the rudimentary nature of the basic knowledge about networks that would enable their designers to predict their behaviors reliably. Its members found it astonishing that a society that invests so much in basic research would be so negligent in focusing such research on the science underlying one of the most fundamental structures on which our modern global economic and political system depends.

Today, the elements of network science are pursued in a wide variety of disciplinary environments. Courses on the structure and function of networks are taught in electrical engineering, computer science, sociology, biology, and physics departments. They focus on different aspects of networks, develop different examples, and employ a diversity of terminologies and mathematical models.

Researchers emphasize their differences to funding agencies because they are supported as ancillaries to other more popular disciplinary programs. The net result is that similar results are discovered independently in each of these environments so that much money and effort is wasted in the process. More importantly, the exceptional quality talent needed to advance such an emergent field will not be attracted in spite of its preeminent national importance. (Think, e.g., of the roles of such individuals as Hans Bethe, Enrico Fermi, Eugene Wigner, Richard Feynman, E. O. Lawrence and Robert Oppenheimer in developing nuclear weapons and nuclear power.)

A second important finding of the Network Science study is that this topic is ripe for the exploitation of an intimate connection between theory and experiment on a large enough scale to be of interest for social and biological networks as well as physical networks.

Several sample experiments of direct interest to the Defense Department's Network Centric Operations initiative are outlined in Appendix E of the Network Science report. Such experiments are no more costly or complex than typical high-energy physics experiments. They offer, however, the promise of developing predictive models of social phenomena useful in such diverse contexts as orchestrating the response to large-scale terrorist attacks or natural disasters and the education of inner city elementary school children.

In summary, Network Science is not only an emerging frontier of theoretical physics it also is a comparable frontier in biological and social research. Moreover, discovering the principles underlying the behaviors as well as structures of complex networks is a topic of extreme social and practical importance in the connected era of the 21st century. The NRC report on Network Science documents the importance of the challenges, and sets forth some promising approaches toward meeting these with national initiatives.


1. Friedman, T. L. The World is Flat: A Brief History of the Twenty-First Century (Farrar, Strauss and Girous, New York, 2005).

2. Bower, J. M. and Bolouri, H. eds. Computational Modeling of Genetic and Biochemical Networks (MIT Press, Cambridge, MA, 2001).

3. Watts, D. J. Six Degrees: The Science of a Connected Age (W. A. Norton, New York, NY 2003).

4. Rheingold, H. Smart Mobs: The Next Social Revolution (Basic Books, Cambridge MA, 2002).

5. National Research Council. Network Science (National Academies Press, Washington, 2005), 108 pp.

6. Boccara, N. Modeling Complex Systems (Springer, New York, 2004), 397 pp

7. Binney, J. J., Dowrick, N. J., Fisher, A. J., Newman, M. E. J. The Theory of Critical Phenomena (Clarendon Press, Oxford, 1992), 464pp.

8. Albert, R. and Barabasi, A.-L. Statistical Mechanics of Complex Networks, Rev. Mod. Phys. 74 47-256 (2002).

9. Newman, M. E. J. The Structure and Function of Complex Networks, SIAM Review 45 167-256 (2003).

Article submitted by:
Arie Bodek
12/3/06; 4:54:04 PM

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