1. Graph Representations
There are two main ways of representing graphs in a computer:
The adjacency matrix representation.
The adjacency list representation.

2. Graph Representations
The adjacency matrix representation:
1 if (v, w)  E
M(v, w) =
0 otherwise
A B C D E F A B C D E F B C A F D E

3. Graph Representations
The adjacency matrix representation:
Space:
|V| bits 2
1 if (v, w)  E
M(v, w) =
0 otherwise
A B C D E F A B C D E F B C A F D E

4. Graph Representations
The adjacency list representation:
L(v) = list of w such that (v, w)  E,
for v  V A B C D E F B D B C A C A B D E F A C E D E C D

5. Graph Representations
The adjacency list representation:
How much space: ? A B C D E F B D B C A C A B D E F A C E D E C D

6. Graph Representations
The adjacency list representation:
Space: a |V| + 2 b |E| a b A B C D E F B D B C A C A B D E F A C E D E C D

7. Graph Representations
The adjacency matrix representation, again,
this time representing a directed graph.
A B C D E F A B C D E F B C A F D E

8. Graph Representations
The adjacency list representation, again,
this time representing a directed graph. A B C D E F B D B C C A E F C D E D

9. Graph Representations
The adjacency list representation, again,
this time representing a directed graph.
How much space? A B C D E F B D B C C A E F C D E D

10. Graph Representations
The adjacency list representation, again,
this time representing a directed graph.
Space: a |V| + b |E| a b A B C D E F B D B C C A E F C D E D