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General network theory rka albert
 

Summary: General network theory
réka albert
Pennsylvania State University
complex web-like structures describe a wide variety of systems of high technologi-
cal and intellectual importance. For example, the cell is best described as a complex net-
work of proteins and small molecules connected by biochemical reactions; the Internet is
a complex network of routers and computers linked by various physical or wireless links;
fads and ideas spread on the social network whose nodes are human beings and edges rep-
resent various social relationships; the world-wide web is an enormous virtual network of
webpages connected by hyperlinks.
a system of elements that interact or regulate each other can be represented by a math-
ematical object called a graph (Bollobás 1979). here graph is not used in its usual meaning
of `diagram of a functional relationship', but as `a collection of nodes and edges', in other
words, a network. at the simplest level, the system's elements are reduced to graph nodes
(also called vertices) and their interactions are reduced to edges connecting pairs of nodes
(see Figure 1, overleaf). a graph at its simplest is a connection of nodes (a, B, C...) and
edges (aC, BC, CD, CJ...). The node arrangement and length of edges does not mat-
ter, only which is connected to which. edges can be either directed, specifying a source
(starting point) and a target (endpoint), or non-directed. Directed edges are suitable for
representing the flow of material or of information, while non-directed edges are used to

  

Source: Albert, Réka - Departments of Biology & Physics, Pennsylvania State University

 

Collections: Biology and Medicine