We can build on top of this: Graph Representation - Adjacency List and Map. We can store source as key in map and pair of destination and weight as adjacency list. We are using int array of size 2 here, as java doesnt still have a good pair class.

Code

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public class Graph {
    private Map<Integer, List<int[]>> adjList = new LinkedHashMap<>();
    private int V;
    private final boolean isDirected;

    public Graph(int n, boolean isDirected) {
        V = n;
        for (int i = 0; i < n; i++) {
            adjMap.put(i, new LinkedList<>());
        }
        this.isDirected = isDirected;
    }

    public boolean addEdge(int i, int j, int w) {
        adjMap.putIfAbsent(i, new LinkedList<>());
        adjMap.get(i).add(new int[]{j, w});
        if (!isDirected) {
            adjMap.putIfAbsent(j, new LinkedList<>());
            adjMap.get(j).add(new int[]{i, w});
        }
        return true;
    }
}