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Unformatted text preview: 2/16 Network models A graph, or network, is defined by two sets: nodes (points, vertices) and arcs (links, edges). Notation: G = ( V , A ), where V is a set of vertices and A is a set of arcs consisting of an ordered pair of vertices (representing a possible direction of motion that may occur between vertices). ? 7 S S S S So S S S S So 7 1 2 3 4 5 6 3/16 Continental Airlines network (as of November 2005) 4/16 Southwest Airlines route network as of 2003 Source: D. Jenkins, editor. Southwest Airlines: An InDepth Review . 5/16 Network models Definition (Chain) A sequence of arcs such that every arc has exactly one vertex in common with the previous arc is called a chain. Definition (Path) A path is a chain in which the terminal node of each arc is identical to the initial node of next arc. 6/16 Network models Undirected graph: edges have no directions (or can be thought of as bidirectional) 1 2 3 4 5 6 7/16 Minimum spanning tree problems Suppose that each arc ( i , j ) in a network has a length associated with it and that arc ( i , j ) represents a way of connecting node i to node j . For example, if each node in a network represents a computer in a computer network, arc ( i , j ) might represent an underground cable that connects computer i to computer j ....
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This note was uploaded on 12/14/2010 for the course ESI 6314 taught by Professor Vladimirlboginski during the Fall '09 term at University of Florida.
 Fall '09
 VLADIMIRLBOGINSKI

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