Graphs, A Quick Intro

• A graph is a mathematial structure used to represent relationships.
• A graph G=(V,E)
  • V is a set of vertexes, or nodes
    • These are the data.
  • E is a set of edges, or connections between vertexes.
• We frequently represent graphs as
  • Circles for the vertexes
  • Lines for the edges.
• In figure 1.6, page 6 the Gale-Shapley algorithm is represened as a graph
  • The nodes are the individual men and women.
  • The edges represent a pairing.
  • A solution represents a grap where each node has exactaly one edge
  • And each edge connects a man vertex with a woman vertex.
• Remember
  • M: {A, B, C}
  • W: {1, 2, 3}
  • A: 1, 2, 3
  • B: 2, 1, 3
  • C 1, 2, 3
  • 1: A, B, C
  • 2: A, C, B
  • 3: A, C, B
  • S: (A, 1) (C, 2) (B, 3)
• 
• We will cover graphs formally in chapter 3.