vector<vector<int>> G;

vector<int> G[N];	// where N is the number of nodes

How about in java? What should I use then?

[trollface mode]

set< pair< T, T > > G;

[/trollface mode]

If you don't want to use vectors, you can write use just 3 arrays. Memory is O(2 * M + N).

To add edge, you can write like that:

void add_edge(int x, int y) {
    len++;
    nx[len] = st[x];
    to[len] = y;

    st[x] = len;
}

And to get all nodes from x:

int v = st[x];
while (v) {
    printf("%d ", to[v]);
    v = nx[v];
}

I'd say it may depend on what tasks you are going to solve on this graph, and how the graph is specified, do you need to handle duplicated edges etc.

For edges and vertices you usually use array of lists, 2d array, list of maps, maps of maps etc.

But sometimes you will want some tricky additional structure like enhanced priority queue (for Dijkstra) or disjoint set (for Cruscal?) etc, depending on algorithm.

So your question is just too vague.

The data structure depends directly on what you want to do with the graph. Sometimes you only need the edges (Bellman-Ford, for example), sometimes a matrix (all pairs sp), an UFSet (MST, keep track of graph connectivity if edges are added), an adjacency list (usually best choice for traversal-related problems)...

Do a lot of graph problems and you will see what kinds of representation exists and how to use them!