# L16_10 - Network models A graph or network is dened by two...

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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). 1 2 3 4 5 6

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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 In-Depth Review .

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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 bi-directional) 1 2 3 4 5 6

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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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