### Quick Facts

• Represents graph with “V” nodes into a $$V x V$$ binary matrix.
• A 1 means the two vertices are connected; and a 0 means they are not connected.

Pros:

• Easy to implement.
• Adding and removing an edge, and checking whether there is an edge from one vertex to another is very efficient. Time complexity is $$O(1)$$.
• Good choice of implementation if the graph is dense and there are a large number of edges.
• By performing operations on the adjacency matrix, we can get important insights into the nature of the graph and the relationship between its vertices.

Cons:

• Takes up $$O(V^2)$$ space. For large graphs, too much memory is consumed. Most real world applications for graphs do not have many connections. Therefore, in these situations, too much space is wasted.
• Adding vertex takes $$O( V^2 )$$ time.

### David Inga

Designed by David Inga in California.