Complexities of Graph Operations

Explore the time complexities of basic graph operations like adding and removing vertices and edges in adjacency lists and adjacency matrices. Learn how each representation impacts performance and when to use each structure for efficient graph manipulation in coding interviews.

We'll cover the following...

- Time complexities
  - Adjacency list
  - Adjacency matrix
- Comparison

Time complexities

Below you can find the time complexities for the four basic graph functions.

In this table, V means the total number of vertices, and E means the total number of edges in the graph.

Operation	Adjacency List	Adjacency Matrix
Add Vertex	$O(1)$	$O(V^2)$

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1.Introduction to Complexity Measures

2.Introduction to Arrays

3.Introduction to Linked Lists

4.Introduction to Stack/Queues

5.Introduction to Graphs

6.Introduction to Trees

7.Trie

8.Introduction to Heap

9.Introduction to Hashing

10.Summary of Data Structures

Complexities of Graph Operations

Time complexities