submit urlsubmit rss feedadd directory

article

In mathematics and computer science, graph theory has for its subject matter the properties of graphs. Informally speaking, a graph is a set of objects called points or vertices connected by links called lines or edges. In a graph proper, which is by default undirected, a line from point A to point B is considered to be the same thing as a line from point B to point A. In a digraph, short for directed graph, the two directions are counted as being distinct arcs or directed edges.

Structures that can be represented as graphs are ubiquitous, and many problems of practical interest can be represented by graphs. The link structure of a website could be represented by a directed graph: the vertices are the web pages available at the website and there's a directed edge from page A to page B if and only if A contains a link to B. The development of algorithms to handle graphs is therefore of major interest in computer science.

A graph structure can be extended by assigning a weight to each edge of the graph. Graphs with weights can be used to represent many different concepts; for example if the graph represents a road network, the weights could represent the length of each road.The only information a weighted graph provides as such is (a) the vertices, (b) the edges and (c) the weights. Therefore the example in which the weights represent the roads' lengths doesn't imply that the weights are merely redundant annotations: there is no actual topographical information associated with the graph, so unlike reading a map, measuring the distances between the vertices is completely meaningless -- without the weights, there would be no way of telling what the distance between the vertices is in real life. A digraph with weighted edges is called a network.

More on [ Graph theory ]


directory of related categories

 

 
 
Graph_Theory RSS feed
Wiley: All New Mathematics & Statistics Titles

Business Math For Dummies
Mary Jane Sterling Mon, 30 Jun 2008 04:00:00 -0000
  The essential desk reference for every business professional or student This easy-to-understand resource explains complex mathematical concepts and formulas and offers clear examples of how they relate to real-world business situations. Featuring practical practice problems to help readers hone their skills, it covers such key topics as working with percents to calculate increases and decreases, Read More...
Uncertainty in Industrial Practice: A Guide to Quantitative Uncertainty Management
Etienne de Rocquigny (Editor), Dr. Nicolas Devictor (Editor), Dr. Stefano Tarantola (Editor) Mon, 30 Jun 2008 04:00:00 -0000
  There is a growing demand from institutional bodies for the justification of industrial methodologies and practices (e.g. safety criteria, environmental protection and control, maintenance and design optimization). Previous books in this area have either been too theoretical, or too specific in their scope. Uncertainty in Industrial Practice aims to provide a practical reference on uncertainty treatment for all types of industry, Read More...
Generalized, Linear, and Mixed Models, 2nd Edition
Charles E. McCulloch, Shayle R. Searle, John M. Neuhaus Mon, 30 Jun 2008 04:00:00 -0000
  An accessible and self-contained introduction to statistical models-now in a modernized new edition Generalized, Linear, and Mixed Models, Second Edition provides an up-to-date treatment of the essential techniques for developing and applying a wide variety of statistical models. The book presents thorough and unified coverage of the theory behind generalized, linear, and mixed models and highlights their similarities and differences in various Read More...
Bayesian Approach to Inverse Problems
Jérôme Idier (Editor) Mon, 30 Jun 2008 04:00:00 -0000
  Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest Read More...
Time Series Analysis: Forecasting and Control, 4th Edition
George E. P. Box, Gwilym M. Jenkins, Gregory C. Reinsel Mon, 30 Jun 2008 04:00:00 -0000
  This is a revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application forecasting, model specification, Read More...
Numerical Methods for Ordinary Differential Equations, 2nd Edition
John Butcher Mon, 23 Jun 2008 04:00:00 -0000
  Authored by one of the world’s leading authorities on numerical methods this update of one of the standard references on numerical analysis, outlines recent developments in the field and presenting a detailed overview of the area. The only book to provide both a detailed treatment of Runge-Kutta methods and a thorough exposition of general linear methods, it also provides practical guidance on solving equations associated with general linear Read More...

 
Subscribe to Math RSS feed

directory of related sites

A Constructive Approach to Graph Theory - Notes on a semiotic approach to constructing isomorphism invariants of graphs by John-Tagore Tevet.

404 A Journey through Intersection Graph County - By Erich Prisner.

A Survey of Distance-Transitive Graphs - By Arjeh M. Cohen.

Capillary Multi-Path Routing in a Network of a Directed Symmetric Graph - By Emin Gabrielyan.

Counting Hamilton Cycles in Product Graphs - By Frans Faase.

Fractal Instances of the Traveling Salesman Problem - By Pablo Moscato.

From the Even Cycle Mystery to the L-Matrix Problem and Beyond - By Michael Brundage.

Getgrats: General Theory of Graph Transformation Systems - A research network funded by the European Commission.

Graph Colorings with Local Constraints - A survey by Zsolt Tuza.

Graphnet Archives - Archives of the Graphnet mailing list from February 1990.

404 Graphs: Theory-Algorithms-Complexity - Resource collection maintained by Thomas Emden-Weinert.

500 Harmonious Colourings - Notes and bibliography by Keith Edwards.

Knight's Tour Problem - Solution for chess boards with upto 32 squares.

Multicommodity Problems - Instances and random generators of multicommodity flow and network design problems.

Network Resources for Colouring a Graph - Resources for formulating and solving coloring problems.

Other Graph Theory and Related Pages - Miscellaneous pages collected by Stephen C. Locke.

Parameters of Directed Strongly Regular Graphs - Parameters, constructions and nonexistence information for directed strongly regular graphs.

Regular Graphs Page - Tables of simple connected k-regular graphs on n vertices and girth at least g.
Meta Description: [ Regular Graphs Page ]

Sandpiles in Graphs - An application of cellular automata by Angela R. Kerns.
Meta Description: [ Sandpiles in Graphs ]

Signed, Gain and Biased Graphs - List of publications and manuscripts annotated by Thomas Zaslavsky.

Spectral Graph Theory - People, publications, research topics, open problems, events and resources.
Meta Description: [ The theory of graph spectra can, in a way, be considered as an attempt to utilize linear algebra including, in particular, the well-developed theory of matrices for the purposes of graph theory and its applications. ]

404 The Four Color Theorem - Computer aided proof of the four color theorem by Neil Robertson, Daniel P. Sanders, Paul Seymour and Robin Thomas.

The Hamiltonian Page - Hamiltonian cycle and path problems, their generalisations and variations.

404 Thrackles - Jon Perry's pages on the thrackle conjecture.

Traveling Salesman Problem - These pages report the history of the TSP and ongoing work to solve large instances.

TSP Generator - Generates a Traveling Salesman Problem map and data for a given set of US cities.

Graph_Theory related videos
of Electrical Engineering, IIT,Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in ... Graph Theory ...
Next Video

 

HOMEADVERTISINGABOUT US

articlesartsbusinesscomputersgameshealthhospitalshomekids & teensnewsmobilephysiciansrecreationreferenceregionalscienceshoppingsocietysportsworld


Submit a Site About Become an Editor