***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` to represent the adjacency list of a vertex, it's not as convenient or intuitive to use a `List` 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: ```javascript 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: ```javascript public List> getEdges() { List> edges = new ArrayList<>(); for (Map.Entry> 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: ```javascript System.out.print("Edges: "); for (Pair 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: ```javascript 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.