A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations, an ecosystem, a living cell, and ultimately the entire universe.
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P(k) of nodes in the network having k connections to other nodes goes for large values of k as
A cascading failure is a failure in a system of interconnected parts in which the failure of one or few parts leads to the failure of other parts, growing progressively as a result of positive feedback. This can occur when a single part fails, increasing the probability that other portions of the system fail. Such a failure may happen in many types of systems, including power transmission, computer networking, finance, transportation systems, organisms, the human body, and ecosystems.
A generegulatory network (GRN) is a collection of molecular regulators that interact with each other and with other substances in the cell to govern the gene expression levels of mRNA and proteins which, in turn, determine the function of the cell. GRN also play a central role in morphogenesis, the creation of body structures, which in turn is central to evolutionary developmental biology (evo-devo).
A wireless mesh network (WMN) is a communications network made up of radio nodes organized in a mesh topology. It can also be a form of wireless ad hoc network.
In mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the nodes or edges possess attributes. Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) components.
A small-world network is a graph characterized by a high clustering coefficient and low distances. On an example of social network, high clustering implies the high probability that two friends of one person are friends themselves. The low distances, on the other hand, mean that there is a short chain of social connections between any two people. Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes grows proportionally to the logarithm of the number of nodes N in the network, that is:
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 graphs but often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research inspired largely by empirical findings of real-world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks.
In the U.S., critical infrastructure protection (CIP) is a concept that relates to the preparedness and response to serious incidents that involve the critical infrastructure of a region or the nation. The American Presidential directive PDD-63 of May 1998 set up a national program of "Critical Infrastructure Protection". In 2014 the NIST Cybersecurity Framework was published after further presidential directives.
A wireless ad hoc network (WANET) or mobile ad hoc network (MANET) is a decentralized type of wireless network. The network is ad hoc because it does not rely on a pre-existing infrastructure, such as routers or wireless access points. Instead, each node participates in routing by forwarding data for other nodes. The determination of which nodes forward data is made dynamically on the basis of network connectivity and the routing algorithm in use.
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. In the particular case of non-overlapping community finding, this implies that the network divides naturally into groups of nodes with dense connections internally and sparser connections between groups. But overlapping communities are also allowed. The more general definition is based on the principle that pairs of nodes are more likely to be connected if they are both members of the same community(ies), and less likely to be connected if they do not share communities. A related but different problem is community search, where the goal is to find a community that a certain vertex belongs to.
Fractal analysis is useful in the study of complex networks, present in both natural and artificial systems such as computer systems, brain and social networks, allowing further development of the field in network science.
Complex interdependence in international relations and international political economy is a concept put forth by Robert Keohane and Joseph Nye in the 1970s to describe the emerging nature of the global political economy. The concept entails that relations between states are becoming increasingly deep and complex. These increasingly complex webs of economic interdependence undermine state power and elevate the influence of transnational non-state actors. These complex relationships can be explored through both the liberal and realism lenses and can later explain the debate of power from complex interdependence.
A Boolean network consists of a discrete set of boolean variables each of which has a Boolean function assigned to it which takes inputs from a subset of those variables and output that determines the state of the variable it is assigned to. This set of functions in effect determines a topology (connectivity) on the set of variables, which then become nodes in a network. Usually, the dynamics of the system is taken as a discrete time series where the state of the entire network at time t+1 is determined by evaluating each variable's function on the state of the network at time t. This may be done synchronously or asynchronously.
An important question in statistical mechanics is the dependence of model behaviour on the dimension of the system. The shortcut model was introduced in the course of studying this dependence. The model interpolates between discrete regular lattices of integer dimension.
Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive and semantic networks, and social networks, considering distinct elements or actors represented by nodes and the connections between the elements or actors as links. The field draws on theories and methods including graph theory from mathematics, statistical mechanics from physics, data mining and information visualization from computer science, inferential modeling from statistics, and social structure from sociology. The United States 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."
Hierarchical network models are iterative algorithms for creating networks which are able to reproduce the unique properties of the scale-free topology and the high clustering of the nodes at the same time. These characteristics are widely observed in nature, from biology to language to some social networks.
Rigidity theory, or topological constraint theory, is a tool for predicting properties of complex networks based on their composition. It was introduced by James Charles Phillips in 1979 and 1981, and refined by Michael Thorpe in 1983. Inspired by the study of the stability of mechanical trusses as pioneered by James Clerk Maxwell, and by the seminal work on glass structure done by William Houlder Zachariasen, this theory reduces complex molecular networks to nodes constrained by rods, thus filtering out microscopic details that ultimately don't affect macroscopic properties. An equivalent theory was developed by P.K. Gupta A.R. Cooper in 1990, where rather than nodes representing atoms, they represented unit polytopes. An example of this would be the SiO tetrahedra in pure glassy silica. This style of analysis has applications in biology and chemistry, such as understanding adaptability in protein-protein interaction networks. Rigidity theory applied to the molecular networks arising from phenotypical expression of certain diseases may provide insights regarding their structure and function.
In network theory, multidimensional networks, a special type of multilayer network, are networks with multiple kinds of relations. Increasingly sophisticated attempts to model real-world systems as multidimensional networks have yielded valuable insight in the fields of social network analysis, economics, urban and international transport, ecology, psychology, medicine, biology, commerce, climatology, physics, computational neuroscience, operations management, and finance.
The Bianconi–Barabási model is a model in network science that explains the growth of complex evolving networks. This model can explain that nodes with different characteristics acquire links at different rates. It predicts that a node's growth depends on its fitness and can calculate the degree distribution. The Bianconi–Barabási model is named after its inventors Ginestra Bianconi and Albert-László Barabási. This model is a variant of the Barabási–Albert model. The model can be mapped to a Bose gas and this mapping can predict a topological phase transition between a "rich-get-richer" phase and a "winner-takes-all" phase.
