Graph Representation in Memory
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Overview
TODO CLRS page 589, DDIA location 1392.
Graph Input Size
When it comes to graphs, the input size is given by two parameters: the number of vertices (n) and the number of edges (m).
For a connected, undirected graph with n vertices, the number of edges ranges from n - 1 and n (n - 1)/2.
Adjacency Lists
Applies to directed and undirected graphs.
An adjacency list representation provides a memory-efficient way of representing sparse graphs, so it is usually the method of choice.
Continue CLRS page 590.
Adjacency Matrices
The edges of a graph are represented using a matrix. Applies to directed and undirected graphs. It can be extended for parallel arcs and weighted graphs.
Space requirements:
Operations supported:
Cases when adjacency matrix representation is preferred:
- dense graphs.
- When we need to tell quickly if there is an edge connecting two given vertices.
CLRS page 590.