Graph Overview

Notes

• A graph is a mathematical structure that shows relationships between items.
• Normally the items are stored in a vertex.
• Normally the relations are edges between these vertexes
• An edge can be
  • undirected or directed
  • weighted or unweighted
• A graph then is a set of edges and vertexes: G = (V,E)
• If there is an edge between two vertexes, then the vertexes are adjacent
• A graph with few connections is called sparse or |E| ≈ |V|
• A dense graph has many connections or |E| ≈ |V|²
  • How many edges are possible? Gauss the Pythagoreans have the answer for us.
• How can we store a graph?
  • In an adjacency list format each vertex has a list of adjacent vertexes and possibly the cost of each edge.
    • This has |E| storage requirement.
  • In an adjacency matrix format a 2d array stores this information
    • This has |V|² storage requirement