1 / 5

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

mika
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related