1. A graph is most dense when E (edges) is closest to $|V|^2$
2. A graph is most sparse when is closer to $|V|$ What does it mean to take the magnitude of the vertices?

Secondly, I am having a hard time conceptualizing why the above two rules are true.

Also can someone elaborate on why if a graph is sparse, it should be represented with an adj list and why if it is dense, it is best to use an adjacency matrix instead?

1. A graph is dense when |E| (edges) is closest to $|V|^2$.
2. A graph is sparse when |E| is closer to $|V|$.

What does it mean to take the magnitude of the vertices? Secondly, I am having a hard time conceptualizing why the above two rules are true.

Also can someone elaborate on why if a graph is sparse, it should be represented with an adj list and why if it is dense, it is best to use an adjacency matrix instead?

1. A graph is most dense when E (edges) is closest to $|V|^2$
2. A graph is most sparse when is closer to $|V|$ What does it mean to take the magnitude of the vertices?

Secondly, I am having a hard time conceptualizing why the above two rules are true. Can someone elaborate on this?

1. A graph is most dense when E (edges) is closest to $|V|^2$
2. A graph is most sparse when is closer to $|V|$ What does it mean to take the magnitude of the vertices?

Secondly, I am having a hard time conceptualizing why the above two rules are true.

Also can someone elaborate on why if a graph is sparse, it should be represented with an adj list and why if it is dense, it is best to use an adjacency matrix instead?