Note :- Had obtained this explaination from Co-Pilot, Hence kindly double check before grasping it blindly

The Pair class in this code is used to represent an edge in the graph. Each edge is a pair of vertices, and the Pair class is a convenient way to group these two vertices together.

While it's true that you can use a List<Integer> to represent the adjacency list of a vertex, it's not as convenient or intuitive to use a List<Integer> to represent an edge. An edge is a connection between two specific vertices, and the order of the vertices matters. A Pair makes it clear that you're dealing with two specific, ordered items.

Let's consider an example. Suppose you have a graph with vertices 1, 2, and 3, and edges (1, 2) and (2, 3). The adjacency list representation of this graph would be:

1: [2]
2: [1, 3]
3: [2]

This tells you which vertices are adjacent to each other, but it doesn't directly tell you what the edges of the graph are. If you want to get a list of edges, you would need to iterate over the adjacency list and create pairs of vertices. This is what the getEdges() method does:

public List<Pair<Integer, Integer>> getEdges() {
    List<Pair<Integer, Integer>> edges = new ArrayList<>();
    for (Map.Entry<Integer, List<Integer>> entry : adjacencyList.entrySet()) {
        int vertex1 = entry.getKey();
        for (int neighbor : entry.getValue()) {
            int vertex2 = neighbor;
            if (vertex1 < vertex2) {
                edges.add(new Pair<>(vertex1, vertex2));
            }
        }
    }
    return edges;
}

This method iterates over the adjacency list and creates a Pair for each edge. The Pair class makes it easy to group the two vertices of each edge together, and the resulting list of pairs represents the list of edges in the graph.

In the main method, this list of edges is printed out:

System.out.print("Edges: ");
for (Pair<Integer, Integer> edge : graph.getEdges()) {
    System.out.print("(" + edge.getFirst() + ", " + edge.getSecond() + ") ");
}
System.out.println();

This prints out the edges of the graph as pairs of vertices, like this:

Edges: (1, 2) (2, 3)

This makes it clear that the graph has two edges, one between vertices 1 and 2, and one between vertices 2 and 3. This would be harder to determine from the adjacency list alone, especially for larger graphs. The Pair class provides a convenient and intuitive way to represent the edges of the graph.