Network science
Encyclopedia
Network science is a new and emerging scientific discipline that examines the interconnections among diverse physical or engineered networks, information networks
, biological networks
, cognitive and semantic networks, 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 study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena."
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 1930s 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 liked a single girl. The feeling was not reciprocated. This network representation of social structure was found so intriguing that it was printed in 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.
In 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 focused 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 loosely defined network topology that contains hub vertices with many connections, that grow in a way to maintain a constant ratio in the number of the connections versus all other nodes. Although many networks, such as the internet, appear to maintain this aspect, other networks have long tailed distributions of nodes that only approximate scale free ratios.
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.
as an operational concept based on network science in 1996. John A. Parmentola, the U.S. Army Director for Research and Laboratory Management, proposed to the Army’s Board on Science and Technology (BAST) on December 1, 2003 that Network Science become a new Army research area. The BAST, the Division on Engineering and Physical Sciences for the National Research Council (NRC) of the National Academies, serves as a convening authority for the discussion of science and technology issues of importance to the Army and oversees independent Army-related studies conducted by the National Academies. The BAST conducted a study to find out whether identifying and funding a new field of investigation in basic research, Network Science, could help close the gap between what is needed to realize Network-Centric Operations and the current primitive state of fundamental knowledge of networks.
As a result, the BAST issued the NRC study in 2005 titled Network Science (referenced above) that defined a new field of basic research in Network Science for the Army. Based on the findings and recommendations of that study and the subsequent 2007 NRC report titled Strategy for an Army Center for Network Science, Technology, and Experimentation, Army basic research resources were redirected to initiate a new basic research program in Network Science. To build a new theoretical foundation for complex networks, some of the key Network Science research efforts now ongoing in Army laboratories address:
As initiated in 2004 by Frederick I. Moxley with support he solicited from David S. Alberts
, the Department of Defense helped to establish the first Network Science Center in conjunction with the U.S. Army at the United States Military Academy. Subsequently, the U.S. Department of Defense has funded numerous research projects in the area of Network Science.
In 2006, the U.S. Army and the United Kingdom (UK) formed the Network and Information Science International Technology Alliance
, a collaborative partnership among the Army Research Laboratory, UK Ministry of Defense and a consortium of industries and universities in the U.S. and UK. The goal of the alliance is to perform basic research in support of Network- Centric Operations across the needs of both nations.
In 2009, the U.S. Army formed the Network Science CTA
, a collaborative research alliance among the Army Research Laboratory
, CERDEC, and a consortium of about 30 industrial R&D labs and universities in the U.S. The goal of the alliance is to develop a deep understanding of the underlying commonalities among intertwined social/cognitive, information, and communications networks, and as a result improve our ability to analyze, predict, design, and influence complex systems interweaving many kinds of networks.
Information networks
Information networks are networks that transmit information in versatile human and technical networks to enhance knowledge, business or social aims. Often they use information technology in contrast to biological neural networks or social networks research...
, biological networks
Biological neural network
In neuroscience, a biological neural network describes a population of physically interconnected neurons or a group of disparate neurons whose inputs or signalling targets define a recognizable circuit. Communication between neurons often involves an electrochemical process...
, cognitive and semantic networks, 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 study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena."
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 KönigsbergSeven Bridges of Königsberg
The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler in 1735 laid the foundations of graph theory and prefigured the idea of topology....
written by Leonhard Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
in 1736. Euler's mathematical description of vertices and edges was the foundation of graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
, a branch of mathematics that studies the properties of pairwise relations in a network structure. The field of graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
continued to develop and found applications in chemistry (Sylvester, 1878).
In the 1930s 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 liked a single girl. The feeling was not reciprocated. This network representation of social structure was found so intriguing that it was printed in The New York Times
The New York Times
The New York Times is an American daily newspaper founded and continuously published in New York City since 1851. The New York Times has won 106 Pulitzer Prizes, the most of any news organization...
(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
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
with Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
and Alfréd Rényi
Alfréd Rényi
Alfréd Rényi was a Hungarian mathematician who made contributions in combinatorics, graph theory, number theory but mostly in probability theory.-Life:...
'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
Social network
A social network is a social structure made up of individuals called "nodes", which are tied by one or more specific types of interdependency, such as friendship, kinship, common interest, financial exchange, dislike, sexual relationships, or relationships of beliefs, knowledge or prestige.Social...
. An alternate approach to network probability structures is the network probability matrix
Network Probability Matrix
The network probability matrix describes the probability structure of a network based on the historical presence or absence of edges in a network. For example, individuals in a social network are not connected to other individuals with uniform random probability. The probability structure is much...
, 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.
In 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
Dynamic Network Analysis
Dynamic network analysis is an emergent scientific field that brings together traditional social network analysis , link analysis and multi-agent systems within network science and network theory. There are two aspects of this field. The first is the statistical analysis of DNA data. The second...
.
More recently other network science efforts have focused on mathematically describing different network topologies. Duncan Watts reconciled empirical data on networks with mathematical representation, describing the small-world network
Small-world network
In mathematics, physics and sociology, a small-world network is a type of mathematical graph in which most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps...
. Albert-László Barabási
Albert-Laszlo Barabasi
Albert-László Barabási is a physicist, best known for his work in the research of network theory. He is the former Emil T...
and Reka Albert developed the scale-free network
Scale-free network
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P of nodes in the network having k connections to other nodes goes for large values of k as...
which is a loosely defined network topology that contains hub vertices with many connections, that grow in a way to maintain a constant ratio in the number of the connections versus all other nodes. Although many networks, such as the internet, appear to maintain this aspect, other networks have long tailed distributions of nodes that only approximate scale free ratios.
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.
Department of Defense Initiatives
The U.S. military first became interested in network-centric warfareNetwork-centric warfare
Network-centric warfare, also called network-centric operations, is a military doctrine or theory of war pioneered by the United States Department of Defense in the 1990's....
as an operational concept based on network science in 1996. John A. Parmentola, the U.S. Army Director for Research and Laboratory Management, proposed to the Army’s Board on Science and Technology (BAST) on December 1, 2003 that Network Science become a new Army research area. The BAST, the Division on Engineering and Physical Sciences for the National Research Council (NRC) of the National Academies, serves as a convening authority for the discussion of science and technology issues of importance to the Army and oversees independent Army-related studies conducted by the National Academies. The BAST conducted a study to find out whether identifying and funding a new field of investigation in basic research, Network Science, could help close the gap between what is needed to realize Network-Centric Operations and the current primitive state of fundamental knowledge of networks.
As a result, the BAST issued the NRC study in 2005 titled Network Science (referenced above) that defined a new field of basic research in Network Science for the Army. Based on the findings and recommendations of that study and the subsequent 2007 NRC report titled Strategy for an Army Center for Network Science, Technology, and Experimentation, Army basic research resources were redirected to initiate a new basic research program in Network Science. To build a new theoretical foundation for complex networks, some of the key Network Science research efforts now ongoing in Army laboratories address:
- Mathematical models of network behavior to predict performance with network size, complexity, and environment
- Optimized human performance required for network-enabled warfare
- Networking within ecosystems and at the molecular level in cells.
As initiated in 2004 by Frederick I. Moxley with support he solicited from David S. Alberts
David S. Alberts
David Stephen Alberts is an American Director of Research for the Office of the Assistant Secretary of Defense for Networks and Information Integration .- Biography :...
, the Department of Defense helped to establish the first Network Science Center in conjunction with the U.S. Army at the United States Military Academy. Subsequently, the U.S. Department of Defense has funded numerous research projects in the area of Network Science.
In 2006, the U.S. Army and the United Kingdom (UK) formed the Network and Information Science International Technology Alliance
International Technology Alliance
The International Technology Alliance is a research program initiated by the UK Ministry of Defence and the US Army Research Laboratory . The research program is intended to run for 10 years...
, a collaborative partnership among the Army Research Laboratory, UK Ministry of Defense and a consortium of industries and universities in the U.S. and UK. The goal of the alliance is to perform basic research in support of Network- Centric Operations across the needs of both nations.
In 2009, the U.S. Army formed the Network Science CTA
Network Science CTA
The Network Science Collaborative Technology Alliance is a collaborative research alliance funded by the US ArmyResearch Laboratory and focused on fundamentalresearch on the critical scientific and technical challenges that...
, a collaborative research alliance among the Army Research Laboratory
Army Research Laboratory
The Army Research Laboratory is the U.S. Army's corporate research laboratory. ARL is headquartered at the Adelphi Laboratory Center in Adelphi, Maryland. Its largest single site is at Aberdeen Proving Ground, Maryland...
, CERDEC, and a consortium of about 30 industrial R&D labs and universities in the U.S. The goal of the alliance is to develop a deep understanding of the underlying commonalities among intertwined social/cognitive, information, and communications networks, and as a result improve our ability to analyze, predict, design, and influence complex systems interweaving many kinds of networks.
See also
- Complex networkComplex networkIn the context of network theory, a complex network is a graph with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in real graphs...
- Collaborative innovation network
- Dynamic network analysisDynamic Network AnalysisDynamic network analysis is an emergent scientific field that brings together traditional social network analysis , link analysis and multi-agent systems within network science and network theory. There are two aspects of this field. The first is the statistical analysis of DNA data. The second...
- Higher category theoryHigher category theoryHigher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities.- Strict higher categories :...
- Immune network theoryImmune network theoryThe immune network theory is a theory of how the adaptive immune system works, that has been developed since 1974 mainly by Niels Jerne and Geoffrey W. Hoffmann. The theory states that the immune system is an interacting network of lymphocytes and molecules that have variable regions...
- Irregular warfareIrregular warfareIrregular warfare is warfare in which one or more combatants are irregular military rather than regular forces. Guerrilla warfare is a form of irregular warfare, and so is asymmetric warfare....
- Network theoryNetwork theoryNetwork theory is an area of computer science and network science and part of graph theory. It has application in many disciplines including statistical physics, particle physics, computer science, biology, economics, operations research, and sociology...
- Network Theory in Risk AssessmentNetwork Theory in Risk AssessmentA network is an abstract structure capturing only the basics of connection patterns and little else. Because it is a generalized pattern, tools developed for analyzing, modeling and understanding networks can theoretically be implemented across disciplines...
- PolytelyPolytelyPolytely can be described as frequently, complex problem-solving situations characterized by the presence of not one, but several goals, endings.Modern societies face an increasing incidence of various complex problems...
- Systems theorySystems theorySystems theory is the transdisciplinary study of systems in general, with the goal of elucidating principles that can be applied to all types of systems at all nesting levels in all fields of research...
Further reading
- "The Burgeoning Field of Network Science," http://themilitaryengineer.com/index.php?option=com_content&task=view&id=88
- S.N. Dorogovtsev and J.F.F. Mendes, Evolution of Networks: From biological networks to the Internet and WWW, Oxford University Press, 2003, ISBN 0-19-851590-1
- Linked: The New Science of Networks, A.-L. Barabási (Perseus Publishing, Cambridge
- Network Science, Committee on Network Science for Future Army Applications, National Research Council. 2005. The National Academies Press (2005)ISBN 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
- Dynamical processes on complex networks, Alain Barrat, Marc Barthelemy, Alessandro Vespignani (Cambridge University Press, 2008) ISBN 978-0-521-87950-7
- Network Science: Theory and Applications, Ted G. Lewis (Wiley, March 11, 2009) ISBN 0470331887
- Nexus: Small Worlds and the Groundbreaking Theory of Networks, Mark Buchanan (W. W. Norton & Company, June 2003) ISBN 0393324427
- Six Degrees: The Science of a Connected Age, Duncan J. Watts (W. W. Norton & Company, February 17, 2004) ISBN 0393325423
External links
- Network Science Center at the U.S. Military Academy at West Point, NY
- http://press.princeton.edu/titles/8114.html
- http://www.cra.org/ccc/NSE.ppt.pdf
- http://www.ifr.ac.uk/netsci08/
- GNET — Group of Complex Systems & Random Networks
- http://www.netsci09.net/
- Cyberinfrastructure
- Prof. Nicholas A Christakis' introduction to network science in Prospect magazine
- Video Lectures on complex networks by Prof. Shlomo HavlinShlomo HavlinShlomo Havlin is a Professor in the Department of Physics at Bar-Ilan University, Ramat-Gan, Israel. He served as President of the Israel Physical Society , Dean of Faculty of Exact Sciences , Chairman, Department of Physics .-Biography:Professor Shlomo Havlin was born in Jerusalem, Israel...