GE330_lect13 - Lecture 13 Network Models I Graphs A graph...

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Lecture 13 Network Models I March 11, 2009
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Graphs A graph is a set of objects called nodes or vertices connected by links called edges . Usually we use G ( N,E ) to denote a graph, where N is the set of all nodes is and E is the set of all edges. In a graph, which is by default undirected , a link from node n to node m is considered to be the same thing as a link from node m to node n . 1 2 3 5 4 In the above graph N = { 1 , 2 , 3 , 4 , 5 } ; E = { (1 , 2) , (1 , 3) , (1 , 5) , (2 , 4) , (2 , 5) , (3 , 4) , (3 , 5) , (4 , 5) } . 2
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Directed Graphs (Digraphs) In a digraph , short for directed graph , a link from node n to node m is considered to be different to a link from node m to node n , we call them arcs or directed edges . Usually we use G ( N,A ) to denote a digraph, where N is the set of all nodes and A is the set of all arcs. In the above directed graph N = { 1 , 2 , 3 , 4 , 5 } ; A = { (1 , 2) , (1 , 3) , (2 , 3) , (2 , 5) , (3 , 4) , (3 , 5) , (4 , 2) , (4 , 5) } . 3
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Consider a graph G ( N,E ), a path is a sequence of nodes such that there is an edge connecting any two successive nodes in this sequence. A path forms a cycle or a loop if the first node and the last node on the path coincide. A graph is connected if for any pair of nodes on the graph, there exists at least one path connecting these two nodes. A tree is a connected graph with no cycles. Given a connected graph, the spanning tree is a tree that is
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This note was uploaded on 08/31/2010 for the course IESE GE 330 taught by Professor Nedich during the Spring '09 term at University of Illinois at Urbana–Champaign.

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GE330_lect13 - Lecture 13 Network Models I Graphs A graph...

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