CSCE423/823 Computer Science & Engineering 423/823 Introduction Design and Analysis of Algorithms Types of Graphs Representations Lecture 03 | Elementary Graph Algorithms (Chapter 22) of Graphs Elementary Graph Algorithms Applications Stephen Scott (Adapted from Vinodchandran N. Variyam) 1 / 29
[email protected] Introduction CSCE423/823 Introduction Types of Graphs are abstract data types that are applicable to numerous Graphs problems Representations of Graphs Can capture entities, relationships between them, the degree of the Elementary relationship, etc. Graph Algorithms This chapter covers basics in graph theory, including representation, Applications and algorithms for basic graph-theoretic problems We'll build on these later this semester 2 / 29 Types of Graphs CSCE423/823 Introduction A (simple, or undirected) graph G = (V; E) consists of V , a Types of nonempty set of vertices and E a set of unordered pairs of distinct Graphs Representations vertices called edges of Graphs D E Elementary V={A,B,C,D,E} Graph Algorithms Applications E={ (A,D),(A,E),(B,D), (B,E),(C,D),(C,E)} A B C 3 / 29 Types of Graphs (2) CSCE423/823 A directed graph (digraph) G = (V; E) consists of V , a nonempty set of vertices and E a set of ordered pairs of distinct vertices called Introduction edges Types of Graphs Representations of Graphs Elementary Graph Algorithms Applications 4 / 29 Types of Graphs (3) CSCE423/823 A weighted graph is an undirected or directed graph with the Introduction additional property that each edge e has associated with it a real Types of number w(e) called its weight Graphs 3 Representations of Graphs Elementary 12 Graph Algorithms 0 Applications -6 7 4 3 Other variations: multigraphs, pseudographs, etc.