Network theory Network theory is the study of graphs as a representation of either symmetric relations or asymmetric relations between discrete objects. In computer science and network science, network theory is a part of graph theory: a network can be de ...

is an area of

applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemat ...

. This page is a list of

network theory Network theory is the study of graphs as a representation of either symmetric relations or asymmetric relations between discrete objects. In computer science and network science, network theory is a part of graph theory: a network can be de ...

topics.

Network theorems

* Max flow min cut theorem *

Menger's theorem In the mathematical discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number of disjoint paths that can be found between any pair of vertices. Proved by Karl Menger in ...

Metcalfe's law Metcalfe's law states that the value of a telecommunications network is proportional to the square of the number of connected users of the system (''n''2). First formulated in this form by George Gilder in 1993, and attributed to Robert Metca ...

Network properties

Centrality In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position. Applications include identifying the most influential person(s) in a social network, k ...

Betweenness centrality In graph theory, betweenness centrality (or "betweeness centrality") is a measure of centrality in a graph based on shortest paths. For every pair of vertices in a connected graph, there exists at least one shortest path between the vertices suc ...

* Closeness

Network theory applications

* Bose-Einstein condensation: a network theory approach

Networks with certain properties

Complex network 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 ...

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''(''k'') of nodes in the network having ''k'' connections to other nodes goes for large values of ''k'' as : P(k ...

Small-world network A small-world network is a type of mathematical graph in which most nodes are not neighbors of one another, but the neighbors of any given node are likely to be neighbors of each other and most nodes can be reached from every other node by a sm ...

* Small world phenomenon

Other terms

* Bottleneck (network) *

Blockmodeling Blockmodeling is a set or a coherent framework, that is used for analyzing social structure and also for setting procedure(s) for partitioning (clustering) social network's units ( nodes, vertices, actors), based on specific patterns, which form ...

Network automaton A network automaton (plural network automata) is a mathematical system consisting of a network of nodes that evolves over time according to predetermined rules. It is similar in concept to a cellular automaton, but much less studied. Stephen W ...

Network effect In economics, a network effect (also called network externality or demand-side economies of scale) is the phenomenon by which the value or utility a user derives from a good or service depends on the number of users of compatible products. Netw ...

* Network flow *

Pathfinder network A pathfinder network is a psychometric scaling method based on graph theory and used in the study of expertise, knowledge acquisition, knowledge engineering, scientific citation patterns, information retrieval, and data visualization. Pathfinder ...

Scalability Scalability is the property of a system to handle a growing amount of work by adding resources to the system. In an economic context, a scalable business model implies that a company can increase sales given increased resources. For example, a ...

* Sorting network * Space syntax *

Spanning tree protocol The Spanning Tree Protocol (STP) is a network protocol that builds a loop-free logical topology for Ethernet networks. The basic function of STP is to prevent bridge loops and the broadcast radiation that results from them. Spanning tree also ...

Strategyproof In game theory, an asymmetric game where players have private information is said to be strategy-proof or strategyproof (SP) if it is a weakly-dominant strategy for every player to reveal his/her private information, i.e. given no information abou ...

Structural cohesion In sociology, structural cohesion is the conception of a useful formal definition and measure of cohesion in social groups. It is defined as the minimal number of actors in a social network that need to be removed to disconnect the group. It is ...

* Vickrey–Clarke–Groves * Tree and hypertree networks

Examples of networks

Bayesian network A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Bay ...

* Bridges of Königsberg *

Computer network A computer network is a set of computers sharing resources located on or provided by network nodes. The computers use common communication protocols over digital interconnections to communicate with each other. These interconnections ar ...

* Ecological network *

Electrical network An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sour ...

Gene regulatory network A gene (or genetic) regulatory 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 fun ...

Global shipping network The global shipping network is the worldwide network of maritime traffic. From a network science perspective ports represent nodes and routes represent lines. Transportation networks have a crucial role in today's economy, more precisely, maritime ...

Neural network A neural network is a network or neural circuit, circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up ...

* Project network *

Petri net A Petri net, also known as a place/transition (PT) net, is one of several mathematical modeling languages for the description of distributed systems. It is a class of discrete event dynamic system. A Petri net is a directed bipartite graph that ...

Semantic network A semantic network, or frame network is a knowledge base that represents semantic relations between concepts in a network. This is often used as a form of knowledge representation. It is a directed or undirected graph consisting of vertices ...

Social network A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors. The social network perspective provides a set of methods for ...

Spin network In physics, a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise way to represent multiline ...

Telecommunications network A telecommunications network is a group of nodes interconnected by telecommunications links that are used to exchange messages between the nodes. The links may use a variety of technologies based on the methodologies of circuit switching, mes ...

Value network A value network is a graphical illustration of social and technical resources within/between organizations and how they are utilized. The nodes in a value network represent people or, more abstractly, roles. The nodes are connected by interaction ...

Workflow A workflow consists of an orchestrated and repeatable pattern of activity, enabled by the systematic organization of resources into processes that transform materials, provide services, or process information. It can be depicted as a sequence ...

Metabolic network A metabolic network is the complete set of metabolic and physical processes that determine the physiological and biochemical properties of a cell. As such, these networks comprise the chemical reactions of metabolism, the metabolic pathways, as ...

Metabolic network modelling Metabolic network modelling, also known as metabolic network reconstruction or metabolic pathway analysis, allows for an in-depth insight into the molecular mechanisms of a particular organism. In particular, these models correlate the genome wi ...

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