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UMass Lowell Computer Science 91.404 Analysis of Algorithms Prof. Karen Daniels Fall, 2001

UMass Lowell Computer Science 91.404 Analysis of Algorithms Prof. Karen Daniels Fall, 2001. Wednesday, 9/26/01 Graph Basics. A. A. B. B. D. F. F. E. E. D. C. C. Introductory Graph Concepts. G= (V,E) Vertex Degree Self-Loops. Undirected Graph No Self-Loops

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UMass Lowell Computer Science 91.404 Analysis of Algorithms Prof. Karen Daniels Fall, 2001

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  1. UMass Lowell Computer Science 91.404Analysis of AlgorithmsProf. Karen DanielsFall, 2001 Wednesday, 9/26/01 Graph Basics

  2. A A B B D F F E E D C C Introductory Graph Concepts • G= (V,E) • Vertex Degree • Self-Loops • Undirected Graph • No Self-Loops • Adjacency is symmetric • Directed Graph (digraph) • Degree: in/out • Self-Loops allowed This treatment follows 91.503 textbook Cormen et al. Some definitions differ slightly from other graph literature.

  3. A A B B A B C D E F A B C D E F D A B C D E F A BC B CEF C D D E BD F E A BC B ACEF C AB D E E BDF F BE A B C D E F F F E E D C C Introductory Graph Concepts:Representations • Undirected Graph • Directed Graph (digraph) Adjacency Matrix Adjacency List Adjacency List Adjacency Matrix This treatment follows 91.503 textbook Cormen et al. Some definitions differ slightly from other graph literature.

  4. A A B B F A B E E F E C D D D C C F Introductory Graph Concepts:Paths, Cycles path <A,B,F> • Path: • length: number of edges • simple: all vertices distinct • Cycle: • Directed Graph: • <v0,v1,...,vk > forms cycle if v0=vk and k>=1 • simple cycle: v1,v2..,vk also distinct • self-loop is cycle of length 1 • Undirected Graph: • <v0,v1,...,vk > forms (simple) cycle if v0=vk and k>=3 • simple cycle: v1,v2..,vk also distinct simple cycle <E,B,F,E> simple cycle <A,B,C,A>= <B,C,A,B> This treatment follows 91.503 textbook Cormen et al. Some definitions differ slightly from other graph literature.

  5. A A A A B B B D D F F F E E E D D C C C C B strongly connected component F E Introductory Graph Concepts:Connectivity connected • Undirected Graph: connected • every pair of vertices is connected by a path • one connected component • connected components: • equivalence classes under “is reachable from” relation • Directed Graph: strongly connected • every pair of vertices is reachable from each other • one stronglyconnected component • strongly connected components: • equivalence classes under “mutually reachable” relation 2 connected components not strongly connected This treatment follows 91.503 textbook Cormen et al. Some definitions differ slightly from other graph literature.

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