Complex network
Encyclopedia
In the context of network theory
, a complex network is a graph
(network
) with non-trivial topological features—features that do not occur in simple networks such as lattices
or random graph
s but often occur in real graphs. The study of complex networks is a young and active area of scientific research inspired largely by the empirical study of real-world networks such as computer network
s and social network
s.
, biological, and technological network
s display substantial non-trivial topological features, with patterns of connection between their elements that are neither purely regular nor purely random. Such features include a heavy tail in the degree distribution
, a high clustering coefficient
, assortativity
or disassortativity among vertices, community structure
, and hierarchical structure
. In the case of directed networks these features also include reciprocity
, triad significance profile and other features. In contrast, many of the mathematical models of networks that have been studied in the past, such as lattices
and random graph
s, do not show these features.
Two well-known and much studied classes of complex networks are scale-free networks and small-world networks, whose discovery and definition are canonical case-studies in the field. Both are characterized by specific structural features—power-law degree distribution
s for the former and short path lengths and high clustering
for the latter. However, as the study of complex networks has continued to grow in importance and popularity, many other aspects of network structure have attracted attention as well.
The field continues to develop at a brisk pace, and has brought together researchers from many areas including mathematics
, physics
, biology
, computer science
, sociology
, epidemiology
, and others. Ideas from network science have been applied to the analysis of metabolic and genetic regulatory networks, the design of robust and scalable communication networks both wired and wireless, the development of vaccination strategies for the control of disease, and a broad range of other practical issues. Research on networks has seen regular publication in some of the most visible scientific journals and vigorous funding in many countries, has been the topic of conferences in a variety of different fields, and has been the subject of numerous books both for the lay person and for the expert.
. The power law implies that the degree distribution of these networks has no characteristic scale. In contrast, network with a single well-defined scale are somewhat similar to a lattice in that every node has (roughly) the same degree. Examples of networks with a single scale include the Erdős–Rényi (ER) random graph
and hypercube
s. In a network with a scale-free degree distribution, some vertices have a degree that is orders of magnitude larger than the average - these vertices are often called "hubs", although this is a bit misleading as there is no inherent threshold above which a node can be viewed as a hub. If there were such a threshold, the network would not be scale-free.
Interest in scale-free networks began in the late 1990s with the apparent discovery of a power-law degree distribution in many real world networks such as the World Wide Web
, the network of Autonomous systems
(ASs), some network of Internet routers, protein interaction networks, email networks, etc. Although many of these distributions are not unambiguously power laws, their breadth, both in degree and in domain, shows that networks exhibiting such a distribution are clearly very different from what you would expect if edges existed independently and at random (a Poisson distribution
). Indeed, there are many different ways to build a network with a power-law degree distribution. The Yule process is a canonical generative process for power laws, and has been known since 1925. However, it is known by many other names due to its frequent reinvention, e.g., The Gibrat principle by Herbert Simon
, the Matthew effect, cumulative advantage and, most recently, preferential attachment
by Barabási
and Albert for power-law degree distributions.
Networks with a power-law degree distribution can be highly resistant to the random deletion of vertices, i.e., the vast majority of vertices remain connected together in a giant component
. Such networks can also be quite sensitive to targeted attacks aimed at fracturing the network quickly. When the graph is uniformly random except for the degree distribution, these critical vertices are the ones with the highest degree, and have thus been implicated in the spread of disease (natural and artificial) in social and communication networks, and in the spread of fads (both of which are modeled by a percolation
or branching process
). While random graphs (ER) have an average distance of order log N between nodes, where N is the number of nodes, scale free graph can have a distance of log log N. Such graphs are called ultra small world networks.
). The small world hypothesis, which was first described by the Hungarian writer Frigyes Karinthy
in 1929, and tested experimentally by Stanley Milgram
(1967), is the idea that two arbitrary people are connected by only six degrees of separation, i.e. the diameter of the corresponding graph of social connections is not much larger than six. In 1998, Duncan J. Watts
and Steven Strogatz
published the first small-world network model, which through a single parameter smoothly interpolates between a random graph to a lattice. Their model demonstrated that with the addition of only a small number of long-range links, a regular graph, in which the diameter is proportional to the size of the network, can be transformed into a "small world" in which the average number of edges between any two vertices is very small (mathematically, it should grow as the logarithm of the size of the network), while the clustering coefficient stays large. It is known that a wide variety of abstract graphs exhibit the small-world property, e.g., random graphs and scale-free networks. Further, real world networks such as the World Wide Web
and the metabolic network also exhibit this property.
In the scientific literature on networks, there is some ambiguity associated with the term "small world." In addition to referring to the size of the diameter of the network, it can also refer to the co-occurrence of a small diameter and a high clustering coefficient
. The clustering coefficient is a metric that represents the density of triangles in the network. For instance, sparse random graphs have a vanishingly small clustering coefficient while real world networks often have a coefficient significantly larger. Scientists point to this difference as suggesting that edges are correlated in real world networks.
A framework for studying interactions between networks was recently established. Due to interdependencies such systems become significantly more vulnerable, with the appearance of cascading failures and a first order percolation transition.
at least 100 times)
Network theory
Network 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...
, a complex network is a graph
Graph (mathematics)
In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges...
(network
Network
-Mathematics:* Graph * Complex network* Structure* Flow network-Electric, electronic, biological, and biosocial: * Electrical network* Computer network* Biological network* Artificial neural network* Social network...
) with non-trivial topological features—features that do not occur in simple networks such as lattices
Lattice graph
The terms lattice graph, mesh graph, or grid graph refer to a number of categories of graphs whose drawing corresponds to some grid/mesh/lattice, i.e., its vertices correspond to the nodes of the mesh and its edges correspond to the ties between the nodes.-Square grid graph:A common type of a...
or random graph
Random graph
In mathematics, a random graph is a graph that is generated by some random process. The theory of random graphs lies at the intersection between graph theory and probability theory, and studies the properties of typical random graphs.-Random graph models:...
s but often occur in real graphs. The study of complex networks is a young and active area of scientific research inspired largely by the empirical study of real-world networks such as computer network
Computer network
A computer network, often simply referred to as a network, is a collection of hardware components and computers interconnected by communication channels that allow sharing of resources and information....
s and 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...
s.
Definition
Most socialSocial 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...
, biological, and technological network
Computer network
A computer network, often simply referred to as a network, is a collection of hardware components and computers interconnected by communication channels that allow sharing of resources and information....
s display substantial non-trivial topological features, with patterns of connection between their elements that are neither purely regular nor purely random. Such features include a heavy tail in the degree distribution
Degree distribution
In the study of graphs and networks, the degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability distribution of these degrees over the whole network.-Definition:...
, a high clustering coefficient
Clustering coefficient
In graph theory, a clustering coefficient is a measure of degree to which nodes in a graph tend to cluster together. Evidence suggests that in most real-world networks, and in particular social networks, nodes tend to create tightly knit groups characterised by a relatively high density of ties...
, assortativity
Assortativity
Assortativity is a preference for a network's nodes to attach to others that are similar or different in some way. Though the specific measure of similarity may vary, network theorists often examine assortativity in terms of a node's degree...
or disassortativity among vertices, community structure
Community structure
In the study of complex networks, a network is said to have community structure if the nodes of the network can be easily grouped into sets of nodes such that each set of nodes is densely connected internally...
, and hierarchical structure
Hierarchy
A hierarchy is an arrangement of items in which the items are represented as being "above," "below," or "at the same level as" one another...
. In the case of directed networks these features also include reciprocity
Reciprocity in network
Theoretical efforts have been made to study the nontrivial properties of complex networks, such as clustering, scale-free degree distribution, community structures, etc. Here Reciprocity is another quantity to specifically characterize directed networks. Link reciprocity measures the tendency of...
, triad significance profile and other features. In contrast, many of the mathematical models of networks that have been studied in the past, such as lattices
Lattice graph
The terms lattice graph, mesh graph, or grid graph refer to a number of categories of graphs whose drawing corresponds to some grid/mesh/lattice, i.e., its vertices correspond to the nodes of the mesh and its edges correspond to the ties between the nodes.-Square grid graph:A common type of a...
and random graph
Random graph
In mathematics, a random graph is a graph that is generated by some random process. The theory of random graphs lies at the intersection between graph theory and probability theory, and studies the properties of typical random graphs.-Random graph models:...
s, do not show these features.
Two well-known and much studied classes of complex networks are scale-free networks and small-world networks, whose discovery and definition are canonical case-studies in the field. Both are characterized by specific structural features—power-law degree distribution
Degree distribution
In the study of graphs and networks, the degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability distribution of these degrees over the whole network.-Definition:...
s for the former and short path lengths and high clustering
Clustering coefficient
In graph theory, a clustering coefficient is a measure of degree to which nodes in a graph tend to cluster together. Evidence suggests that in most real-world networks, and in particular social networks, nodes tend to create tightly knit groups characterised by a relatively high density of ties...
for the latter. However, as the study of complex networks has continued to grow in importance and popularity, many other aspects of network structure have attracted attention as well.
The field continues to develop at a brisk pace, and has brought together researchers from many areas including mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, biology
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...
, computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
, sociology
Sociology
Sociology is the study of society. It is a social science—a term with which it is sometimes synonymous—which uses various methods of empirical investigation and critical analysis to develop a body of knowledge about human social activity...
, epidemiology
Epidemiology
Epidemiology is the study of health-event, health-characteristic, or health-determinant patterns in a population. It is the cornerstone method of public health research, and helps inform policy decisions and evidence-based medicine by identifying risk factors for disease and targets for preventive...
, and others. Ideas from network science have been applied to the analysis of metabolic and genetic regulatory networks, the design of robust and scalable communication networks both wired and wireless, the development of vaccination strategies for the control of disease, and a broad range of other practical issues. Research on networks has seen regular publication in some of the most visible scientific journals and vigorous funding in many countries, has been the topic of conferences in a variety of different fields, and has been the subject of numerous books both for the lay person and for the expert.
Scale-free networks
A network is named scale-free if its degree distribution, i.e., the probability that a node selected uniformly at random has a certain number of links (degree), follows a particular mathematical function called a power lawPower law
A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...
. The power law implies that the degree distribution of these networks has no characteristic scale. In contrast, network with a single well-defined scale are somewhat similar to a lattice in that every node has (roughly) the same degree. Examples of networks with a single scale include the Erdős–Rényi (ER) random graph
Erdos–Rényi model
In graph theory, the Erdős–Rényi model, named for Paul Erdős and Alfréd Rényi, is either of two models for generating random graphs, including one that sets an edge between each pair of nodes with equal probability, independently of the other edges...
and hypercube
Hypercube
In geometry, a hypercube is an n-dimensional analogue of a square and a cube . It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.An...
s. In a network with a scale-free degree distribution, some vertices have a degree that is orders of magnitude larger than the average - these vertices are often called "hubs", although this is a bit misleading as there is no inherent threshold above which a node can be viewed as a hub. If there were such a threshold, the network would not be scale-free.
Interest in scale-free networks began in the late 1990s with the apparent discovery of a power-law degree distribution in many real world networks such as the World Wide Web
World Wide Web
The World Wide Web is a system of interlinked hypertext documents accessed via the Internet...
, the network of Autonomous systems
Autonomous system (Internet)
Within the Internet, an Autonomous System is a collection of connected Internet Protocol routing prefixes under the control of one or more network operators that presents a common, clearly defined routing policy to the Internet....
(ASs), some network of Internet routers, protein interaction networks, email networks, etc. Although many of these distributions are not unambiguously power laws, their breadth, both in degree and in domain, shows that networks exhibiting such a distribution are clearly very different from what you would expect if edges existed independently and at random (a Poisson distribution
Poisson distribution
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since...
). Indeed, there are many different ways to build a network with a power-law degree distribution. The Yule process is a canonical generative process for power laws, and has been known since 1925. However, it is known by many other names due to its frequent reinvention, e.g., The Gibrat principle by Herbert Simon
Herbert Simon
Herbert Alexander Simon was an American political scientist, economist, sociologist, and psychologist, and professor—most notably at Carnegie Mellon University—whose research ranged across the fields of cognitive psychology, cognitive science, computer science, public administration, economics,...
, the Matthew effect, cumulative advantage and, most recently, preferential attachment
Preferential attachment
A preferential attachment process is any of a class of processes in which some quantity, typically some form of wealth or credit, is distributed among a number of individuals or objects according to how much they already have, so that those who are already wealthy receive more than those who are not...
by 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 Albert for power-law degree distributions.
Networks with a power-law degree distribution can be highly resistant to the random deletion of vertices, i.e., the vast majority of vertices remain connected together in a giant component
Giant component
In network theory, a giant component is a connected component of a given random graph that contains a constant fraction of the entire graph's vertices....
. Such networks can also be quite sensitive to targeted attacks aimed at fracturing the network quickly. When the graph is uniformly random except for the degree distribution, these critical vertices are the ones with the highest degree, and have thus been implicated in the spread of disease (natural and artificial) in social and communication networks, and in the spread of fads (both of which are modeled by a percolation
Percolation
In physics, chemistry and materials science, percolation concerns the movement and filtering of fluids through porous materials...
or branching process
Branching process
In probability theory, a branching process is a Markov process that models a population in which each individual in generation n produces some random number of individuals in generation n + 1, according to a fixed probability distribution that does not vary from individual to...
). While random graphs (ER) have an average distance of order log N between nodes, where N is the number of nodes, scale free graph can have a distance of log log N. Such graphs are called ultra small world networks.
Small-world networks
A network is called a small-world network by analogy with the small-world phenomenon (popularly known as six degrees of separationSix degrees of separation
Six degrees of separation refers to the idea that everyone is on average approximately six steps away, by way of introduction, from any other person on Earth, so that a chain of, "a friend of a friend" statements can be made, on average, to connect any two people in six steps or fewer...
). The small world hypothesis, which was first described by the Hungarian writer Frigyes Karinthy
Frigyes Karinthy
Frigyes Karinthy was a Hungarian author, playwright, poet, journalist, and translator. He was the first proponent of the six degrees of separation concept, in his 1929 short story, Chains . Karinthy remains one of the most popular Hungarian writers...
in 1929, and tested experimentally by Stanley Milgram
Stanley Milgram
Stanley Milgram was an American social psychologist most notable for his controversial study known as the Milgram Experiment. The study was conducted in the 1960s during Milgram's professorship at Yale...
(1967), is the idea that two arbitrary people are connected by only six degrees of separation, i.e. the diameter of the corresponding graph of social connections is not much larger than six. In 1998, Duncan J. Watts
Duncan J. Watts
Duncan J. Watts is an Australian researcher and a principal research scientist at Yahoo! Research, where he directs the Human Social Dynamics group. He is also a past external faculty member of the Santa Fe Institute and a former professor of sociology at Columbia University, where he headed the...
and Steven Strogatz
Steven Strogatz
Steven Henry Strogatz is an American mathematician and the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University...
published the first small-world network model, which through a single parameter smoothly interpolates between a random graph to a lattice. Their model demonstrated that with the addition of only a small number of long-range links, a regular graph, in which the diameter is proportional to the size of the network, can be transformed into a "small world" in which the average number of edges between any two vertices is very small (mathematically, it should grow as the logarithm of the size of the network), while the clustering coefficient stays large. It is known that a wide variety of abstract graphs exhibit the small-world property, e.g., random graphs and scale-free networks. Further, real world networks such as the World Wide Web
World Wide Web
The World Wide Web is a system of interlinked hypertext documents accessed via the Internet...
and the metabolic network also exhibit this property.
In the scientific literature on networks, there is some ambiguity associated with the term "small world." In addition to referring to the size of the diameter of the network, it can also refer to the co-occurrence of a small diameter and a high clustering coefficient
Clustering coefficient
In graph theory, a clustering coefficient is a measure of degree to which nodes in a graph tend to cluster together. Evidence suggests that in most real-world networks, and in particular social networks, nodes tend to create tightly knit groups characterised by a relatively high density of ties...
. The clustering coefficient is a metric that represents the density of triangles in the network. For instance, sparse random graphs have a vanishingly small clustering coefficient while real world networks often have a coefficient significantly larger. Scientists point to this difference as suggesting that edges are correlated in real world networks.
A framework for studying interactions between networks was recently established. Due to interdependencies such systems become significantly more vulnerable, with the appearance of cascading failures and a first order percolation transition.
Researchers and scientists
(with papers on complex networks citedat least 100 times)
- Réka Albert
- Luis Amaral
- Alex Arenas
- Albert-László BarabásiAlbert-Laszlo BarabasiAlbert-László Barabási is a physicist, best known for his work in the research of network theory. He is the former Emil T...
- Alain Barrat
- Marc Barthelemy
- Carl BergstromCarl BergstromCarl T. Bergstrom is a theoretical and evolutionary biologist and a professor at the University of Washington , with a secondary appointment at the Santa Fe Institute. His work concerns the flow of information through biological and social networks and the ecology and evolution, including the...
- Stefano Boccaletti
- Guido CaldarelliGuido CaldarelliGuido Caldarelli is an Italian physicist and associate professor at CNR. He is married with two children and lives in Rome.-Biography:Caldarelli received his Ph.D...
- Sergey Dorogovtsev
- Roger Guimerà
- 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...
- Jon KleinbergJon Kleinberg-External links:**** Stephen Ibaraki*Yury Lifshits,...
- José Mendes
- Yamir Moreno
- Adilson E. MotterAdilson E. MotterAdilson E. Motter, born January 1, 1974, is a Brazilian-born U.S.-based scientist working at Northwestern University, where he has helped develop the concept of synthetic rescue in network biology as well as methods to control the nonlinear dynamics of complex networks...
- Mark NewmanMark NewmanMark Newman is a British physicist and Paul A. M. Dirac Professor of Physics at the University of Michigan, as well as an external faculty member of the Santa Fe Institute...
- Sidney RednerSidney RednerSidney Redner is a Canadian-born physicist and professor of physics at Boston University. Redner has published over 200 journal articles, authored a book titled A Guide to First-Passage Processes , and coauthored a book titled A Kinetic View of Statistical Physics with Pavel L. Krapivsky and Eli...
- Martin Rosvall
- Kim Sneppen
- H. Eugene StanleyH. Eugene StanleyHarry Eugene Stanley is an American physicist and University Professor at Boston University. He has made seminal contributions to statistical physics and is one of the pioneers of interdisciplinary science...
- Steven StrogatzSteven StrogatzSteven Henry Strogatz is an American mathematician and the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University...
- Alessandro VespignaniAlessandro VespignaniAlessandro Vespignani is an Italian physicist and Sternberg Distinguished Professor of Physics, Computer Science and Health Sciences at Northeastern University. Vespignani is known for his work on complex networks, and particularly for work on the applications of network theory to the spread of...
- Duncan J. WattsDuncan J. WattsDuncan J. Watts is an Australian researcher and a principal research scientist at Yahoo! Research, where he directs the Human Social Dynamics group. He is also a past external faculty member of the Santa Fe Institute and a former professor of sociology at Columbia University, where he headed the...
- Yi-Cheng Zhang
See also
- Complex adaptive systemComplex adaptive systemComplex adaptive systems are special cases of complex systems. They are complex in that they are dynamic networks of interactions and relationships not aggregations of static entities...
- Complex SystemsComplex systemsComplex systems present problems in mathematical modelling.The equations from which complex system models are developed generally derive from statistical physics, information theory and non-linear dynamics, and represent organized but unpredictable behaviors of systems of nature that are considered...
- Complexity Science
- 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...
- 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 scienceNetwork scienceNetwork 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,...
- Percolation theoryPercolation theoryIn mathematics, percolation theory describes the behavior of connected clusters in a random graph. The applications of percolation theory to materials science and other domains are discussed in the article percolation.-Introduction:...
- Random graphRandom graphIn mathematics, a random graph is a graph that is generated by some random process. The theory of random graphs lies at the intersection between graph theory and probability theory, and studies the properties of typical random graphs.-Random graph models:...
Books
- Albert-László Barabási, Linked: How Everything is Connected to Everything Else, 2004, ISBN 0-452-28439-2
- Alain Barrat, Marc Barthelemy, Alessandro Vespignani, Dynamical processes on complex networks, Cambridge University Press, 2008, ISBN 978-0-521-87950-7
- Stefan Bornholdt (Editor) and Heinz Georg Schuster (Editor), Handbook of Graphs and Networks: From the Genome to the Internet, 2003, ISBN 3-527-40336-1
- Guido Caldarelli, Scale-Free Networks Oxford University Press, 2007, ISBN 0-19-921151-7
- Reuven Cohen and Shlomo Havlin, Complex Networks: Structure, Robustness and Function, Cambridge University Press, 2010, ISBN 978-0-521-84156-6
- 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
- Mark Newman, Networks: An Introduction, Oxford University Press, 2010, ISBN 978-0-199-20665-0
- Mark Newman, Albert-László Barabási, and Duncan J. Watts, The Structure and Dynamics of Networks, Princeton University Press, Princeton, 2006, ISBN 978-0-691-11357-9
- R. Pastor-Satorras and A. Vespignani, Evolution and Structure of the Internet: A statistical physics approach, Cambridge University Press, 2004, ISBN 0-521-82698-5
- Duncan J. Watts, Six Degrees: The Science of a Connected Age, W. W. Norton & Company, 2003, ISBN 0-393-04142-5
- Duncan J. Watts, Small Worlds: The Dynamics of Networks between Order and Randomness, Princeton University Press, 2003, ISBN 0-691-11704-7
External links
- imGraph Free Excel add-in for drawing graphs.
- Network Science — United States Military Academy - Network Science Center
- Resources in Complex Networks — University of São Paulo - Institute of Physics at São Carlos
- Cx-Nets — Complex Networks Collaboratory
- Networks Wiki
- GNET — Group of Complex Systems & Random Networks
- UCLA Human Complex Systems Program
- New England Complex Systems Institute
- Santa Fe Institute Networks Group
- Barabasi Networks Group
- Cosin Project Codes, Papers and Data on Complex Networks
- Complex network on arxiv.org
- http://supernet.som.umass.edu — Anna Nagurney's Virtual Center for Supernetworks
- BIOREL resource for quantitative estimation of the network bias in relation to external information
- Complexity Virtual Laboratory (VLAB)
- complexnetworks.fr — French computer science research group on networks
- 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...
- A short course 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...