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Unformatted text preview: Graph Algorithms Definitions G=(V,E) V is a set of vertices or nodes E is a set of edges with each edge connecting two vertices Edges are denoted as 2-tuples (u,v), where u, v V G is an undirected graph is edges are unordered 2-tuples G is a directed graph if edges are ordered 2-tuples Undirected edge (u,v) is incident on vertices u and v u and v are adjacent to each other Directed edge (u,v) is incident from u to v, and v is adjacent to u A path from u to v is a sequence <v , v 1 , , v k > of vertices, where v = u and v k =v and (v i ,v i+1 ) E for 0 i<k Length of the path is then number edges in the path CS 6643 F '11 Lec 26 2 Definitions Path (u,v) Exists if v is reachable from u Is simple if all intermediate vertices are distinct Is a cycle if v = v k G is connected if there is a path from any vertex to any other vertex complete graph has all possible edges A complete graph has all possible edges Every vertex is adjacent to all other vertices A forest is an acyclic graph A tree is a connected acyclic graph A weighted graph has weights for each edge G=(V,E,w) is a weigthed graph such that w: E-> is a valid function CS 6643 F '11 Lec 26...
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- Fall '08