Representation

• Edge List
  • Form a list of vertices
  • Form a list of edges
  • Each edge has a pointer to the two endpoints
  • In a undirected graph, order doesn't matter, represent each edge once
  • In a directed graph, first pointer points to start point, second pointer points to endpoint of the edge.
  • Direct access from an edge to a vertex
  • Bad access from a vertex to an edge
  • Really bad for the operation Adjacent(u,v) which tells us if u and v are adjacent.
  • Also bad for finding all of the incident edges of a vertex.
  • Not really very good, we often need to find an edge from a vertex, not the other way around.
  • O(|E|+|V|)
• Adjacency Lists
  • Store vertices in an array
  • Each has a list of adjacent edges
  • This list is just the index to the vertex that is adjacent, plus perhaps the weight.
  • Directed and undirected graphs, this is the same.
  • To see if u is adjacent to v, search u's list for link to v
  • To find all incident edges, just traverse the list.
  • This is good for sparse graphs
  • This is not good for "Which cities does Route 6 connect?"
  • But we usually don't ask that.
  • It is not good for dense, or fully connected graphs
  • Because each edge is represented twice.
  • O(|E|+|V|)
• Adjacency Matrix
  • Form a matrix (or grid)
  • Vertices for horizontal and vertical indices
  • If there is a path from u to v, at Adj[u,v] put a 1
  • Or the weight if we are talking about a weighted graph
  • If it is an undirected graph, put a 1 (or the weight) at Adj[v,u]
  • O(|V|²)