What is better, adjacency lists or adjacency matrices for graph problems in C++?

Question

What is better, adjacency lists or adjacency matrix, for graph problems in C++? What are the advantages and disadvantages of each?

Answer 1

It depends on the problem.

Adjacency Matrix

• Uses O(n^2) memory
• It is fast to lookup and check for presence or absence of a specific edge
  between any two nodes O(1)
• It is slow to iterate over all edges
• It is slow to add/delete a node; a complex operation O(n^2)
• It is fast to add a new edge O(1)

Adjacency List

• Memory usage depends on the number of edges (not number of nodes),
  which might save a lot of memory if the adjacency matrix is sparse
• Finding the presence or absence of specific edge between any two nodes
  is slightly slower than with the matrix O(k); where k is the number of neighbors nodes
• It is fast to iterate over all edges because you can access any node neighbors directly
• It is fast to add/delete a node; easier than the matrix representation
• It fast to add a new edge O(1)