Adjacency matrices are not always the best way to represent graphs because they have some problems:

1. Wasted Space: For big graphs that don't have many connections (called sparse graphs), an adjacency matrix can use a lot of memory. It takes up $O(n^2)$ space, where $n$ is the number of points (or vertices) in the graph. This can lead to a lot of empty space being used.

2. Cumbersome Edge Changes: When you want to add or remove connections (called edges), it can be quick to do—only $O(1)$ time. But, using the matrix still takes up more memory than needed.

3. Checking for Connections: For some tasks that need to check every edge, having an adjacency matrix helps because you can find out if an edge exists very quickly, in $O(1)$ time.

To solve these problems, you might want to try other ways of representing the graph, like edge lists or compressed row storage. These methods are better for saving space, especially when the graph is sparse.