Adjacency List - Visual Example

Nodes: $1$, $2$, $3$. Edges: ($1$-$2$) and ($2$-$3$). The List looks like this:

1: [2]
2: [1, 3]
3: [2]

Notice how much smaller this is? You do not store any zeros. Node $1$ only lists node $2$ because that is its only neighbor. Node $2$ lists both $1$ and $3$ because it connects to both. If you had $1000$ nodes but only $10$ edges, you would store roughly $20$ entries total instead of $1$,$000$,$000$ cells. That is the power of adjacency lists.