Graphs 1.1 - Graphs 337 LAX CSE 2011 Prof. J. Elder ORD 802...

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Unformatted text preview: Graphs 337 LAX CSE 2011 Prof. J. Elder ORD 802 SFO 1843 1233 -1- DFW Last Updated: 4/1/10 10:16 AM Applications Electronic circuits Printed circuit board Integrated circuit Transportation networks Highway network Flight network Computer networks Local area network Internet Web Databases Entity-relationship diagram CSE 2011 Prof. J. Elder -2- Last Updated: 4/1/10 10:16 AM Graphs A graph is a pair (V, E), where V is a set of nodes, called vertices E is a collection of pairs of vertices, called edges Vertices and edges are positions and store elements Example: A vertex represents an airport and stores the three-letter airport code An edge represents a flight route between two airports and stores the mileage of the route 2555 337 HNL LAX ORD 849 802 SFO 1843 1233 DFW PVD LGA 1120 MIA CSE 2011 Prof. J. Elder -3- Last Updated: 4/1/10 10:16 AM Edge Types Directed edge ordered pair of vertices (u,v) first vertex u is the origin second vertex v is the destination ORD e.g., a flight flight AA 1206 PVD Undirected edge unordered pair of vertices (u,v) e.g., a flight route 849 miles ORD PVD Directed graph (Digraph) all the edges are directed e.g., route network Undirected graph all the edges are undirected e.g., flight network CSE 2011 Prof. J. Elder -4- Last Updated: 4/1/10 10:16 AM Vertices and Edges End vertices (or endpoints) of an edge U and V are the endpoints of a Edges incident on a vertex a, d, and b are incident on V a V b h Adjacent vertices d U U and V are adjacent X c Degree of a vertex X has degree 5 e W Parallel edges j Z i g f h and i are parallel edges Y Self-loop j is a self-loop CSE 2011 Prof. J. Elder -5- Last Updated: 4/1/10 10:16 AM ...
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