Graph representation

Title

Description:

1. Adjacency matrix:
   • A $n\times n$ matrix which has 1 at $[u][v]$ if $u$ points to $v$, otherwise 0
   • If the graph is undirected, then $a_{ij}=a_{ji}$ and the matrix 𝐴 is symmetric about the diagonal.
     • Can be waste of memory
2. Adjacency list:
   • 1 list for each vertex and it is 1 (or the weight) if it has edge to $u$
   • $E_v=\{u|(v,u)\in E\}$
3. Edge list:
   • A list of all the edges, denoted by starting vertex and ending vertex
   • eg. [‘A’. ‘C’]

small quiz

• True or False?: For sparse graph (not so many edges), adjacent list and edge list are more memory efficient than adjacency matrix. ⇒ True
• adj matrix has to store a lot of unnecessary zeros of unconnected vertices