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graph theory |
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graph theoryMathematical theory of networks. A graph consists of vertices (also called points or nodes) and edges (lines) connecting certain pairs of vertices. An edge that connects a node to itself is called a loop. In 1735 Leonhard Euler published an analysis of an old puzzle concerning the possibility of crossing every one of seven bridges (no bridge twice) that span a forked river flowing past an island. Euler's proof that no such path exists and his generalization of the problem to all possible networks are now recognized as the origin of both graph theory and topology. Since the mid-20th century, graph theory has become a standard tool for analyzing and designing communications networks, power transmission systems, transportation networks, and computer architectures. |
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Mathematician Leonhard Euler famously attacked this problem in 1736, using graph theory to show that there is no route through the city of Konigsberg, Germany, that traverses each of its seven bridges just once. In choosing deployment areas for emergency rescue forces and assets, it is expedient to use graph theory. Molecular biologists are faced with an unprecedented quantity of data as a result of new technologies requiring the use of advanced computational techniques from unfamiliar areas of mathematics such as computer science, knot theory, and graph theory, whereas proteomics requires combinatorial geometry, thermodynamics, and other areas of physics and chemistry. |
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