Network science

Network science is a new and emerging scientific discipline that examines the interconnections among diverse physical, informational, biological, cognitive, and social networks. This field of science seeks to discover common principles, algorithms and tools that govern network behavior. The National Research Council defines Network Science as "the organized knowledge of networks based on their study using the scientific method."

Several U.S. governmental agencies such as the Department of Defense and the National Science foundation have recently begun to fund research in this field. The U.S. Military Academy has been teaching the subject matter to cadets and has formed a Network Science Center to facilitate education and research within the Army. The Army is also in the process of establishing a research center for Network Science at Aberdeen Proving Grounds. In addition, several universities are conducting active research in network science, such as Carnegie Mellon University, Northeastern University, and the University of Pennsylvania.

Sub disciplines of network science include dynamic network analysis, social network analysis, the study of complex networks, network optimization, network biology, and graph theory.

In September 2006, scientists from several universities initiated the International Council On Network Science (ICONS). This society aims to promote and facilitate the study and education of network science.

Background and history

The study of networks has emerged in diverse disciplines as a means of analyzing complex relational data. The earliest known paper in this field is the famous Seven Bridges of Königsberg written by Leonhard Euler in 1736. Euler's mathematical description of vertices and edges was the foundation of Graph Theory, a branch of mathematics that studies the properties of pairwise relations in a network structure. The field of Graph Theory continued to develop and found applications in chemistry (Sylvester, 1878).

In the 1930's Jacob Moreno, a psychologist in the Gestalt tradition, arrived in the United States. He developed the sociogram and presented it to the public in April 1933 at a convention of medical scholars. Moreno claimed that "before the advent of sociometry no one knew what the interpersonal structure of a group 'precisely' looked like (Moreno, 1953). The sociogram was a representation of the social structure of a group of elementary school students. The boys were friends of boys and the girls were friends of girls with the exception of one boy who said he like a single girl. The feeling was not reciprocated. This network representation of social structure was found so intriguing that it was printed in the The New York Times (April 3, 1933, page 17). The sociogram has found many applications and has grown into the field of social network analysis.

Probabilistic theory in Network Science developed as an off-shoot of Graph Theory with Paul Erdős and Alfréd Rényi's eight famous papers on random graphs. For social networks the exponential random graph model or p* graph is a notational framework used to represent the probability space of a tie occurring in a social network. An alternate approach to network probability structures is the Network Probability Matrix, which models the probability of edges occurring in a network, based on the historic presence or absence of the edge in a sample of networks.

The U.S. military became interested in Network-centric warfare as an operational concept based on network science in 1996. Subsequently, the U.S. Department of Defense has funded numerous research projects in the area of Network Science.

In the 1998, David Krackhardt and Kathleen Carley introduced the idea of a meta-network with the PCANS Model. They suggest that "all organizations are structured along these three domains, Individuals, Tasks, and Resources. Their paper introduced the concept that networks occur across multiple domains and that they are interrelated. This field has grown into another sub-discipline of network science called Dynamic Network Analysis.

More recently other network science efforts have focussed on mathematically describing different network topologies. Duncan Watts reconciled empirical data on networks with mathematical representation, describing the small-world network. Albert-László Barabási and Reka Albert developed the scale-free network which is a topology that contains hub vertices with many connections, while most vertices have relatively few connections.

Today, network science is an exciting and growing field. Scientists from many diverse fields are working together. Network science holds the promise of increasing collaboration across disciplines, by sharing data, algorithms, and software tools.

Further reading

• http://www.netscience.usma.edu/NSW/Papers/Network_Science_Report_Vol1No1.pdf
• http://press.princeton.edu/titles/8114.html
• http://www.cra.org/ccc/NSE.ppt.pdf
• http://www.ifr.ac.uk/netsci08/
• http://www.netscience.usma.edu

References

• "Understanding Network Science," http://www.zangani.com/blog/2007-1030-networkingscience
• Linked: The New Science of Networks, A.-L. Barabási (Perseus Publishing, Cambridge (2002).
• Network Science, The National Academies Press (2005)ISBN-10: 0-309-10026-7
• Network Science Bulletin, USMA (2007) ISBN 978-1-934808-00-9
• The Structure and Dynamics of Networks Mark Newman, Albert-László Barabási, & Duncan J. Watts (The Princeton Press, 2006)ISBN 0-691-11357-2