Adjacency matrix

Adjacency matrices are a popular representation for graphs in algorithmic problems, where for a graph with N nodes, it can be stored as an array int adj[N][N]. Each value adj[a][b] indicates whether the graph contains an edge from nodes a to b. For an unweighted graph, it contains a Boolean value. For a weighted graph, it contains the edge weight.

Implications

Matrix representations are ideal for dense graphs, i.e., if $|E|$ is close to $|V{|}^2$. Main drawback of adjacency matrices is that the matrix contains $n^2$ elements, and if the graph isn’t dense, then most of them are zero.