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Network (mathematics)

 

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Network (mathematics)



 
 
In graph theory
Graph theory

In mathematics and computer science, graph theory is the study of graph : mathematical structures used to model pairwise relations between objects from a certain collection....
, a network is a digraph
Directed graph

A directed graph or digraph is a pair G= of:* a Set V, whose element are called vertices or nodes,* a set A of ordered pairs of vertices, called arcs, directed edges, or arrows....
 with weighted edges. These networks have become an especially useful concept in analysing the interaction between biology
Biology

Biology is a branch of the natural sciences concerned with the study of living organisms and their interaction with each other and their environment ....
 and mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
. Using networks of all types; various applications based on the creativity of the mathematician along with their environment can be evaluated in all sorts of manners. Some may visualize networks in various contexts to feel the network which the nodes belong; creating an environment for the nodes to belong is essential to the mathematical evaluation and furthermore the mathemation belonging to the environment, just as the networks nodes.

Use of many space models to create the complexity of the environment is useful when analysing networks.






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Encyclopedia


In graph theory
Graph theory

In mathematics and computer science, graph theory is the study of graph : mathematical structures used to model pairwise relations between objects from a certain collection....
, a network is a digraph
Directed graph

A directed graph or digraph is a pair G= of:* a Set V, whose element are called vertices or nodes,* a set A of ordered pairs of vertices, called arcs, directed edges, or arrows....
 with weighted edges. These networks have become an especially useful concept in analysing the interaction between biology
Biology

Biology is a branch of the natural sciences concerned with the study of living organisms and their interaction with each other and their environment ....
 and mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
. Using networks of all types; various applications based on the creativity of the mathematician along with their environment can be evaluated in all sorts of manners. Some may visualize networks in various contexts to feel the network which the nodes belong; creating an environment for the nodes to belong is essential to the mathematical evaluation and furthermore the mathemation belonging to the environment, just as the networks nodes.

Use of many space models to create the complexity of the environment is useful when analysing networks. Some examples could be linear, Cartesian, three dimensional, n-dimensional, along with models of expanding and contracting environments, furthermore with the growth or decay of the beings in the network, allow for the various types of situations to be modelled to the specifications of the problem.

See also

  • Network theory
    Network theory

    Network theory is an area of applied mathematics and part of graph theory. It has application in many disciplines including particle physics, computer science, biology, economics, operations research, and sociology....
  • Road coloring problem