```#ifndef GRAPH_H
#define GRAPH_H

#include "Edge.h" // Defined in Listing 26.1
#include "Tree.h" // Defined in Listing 26.4
#include <vector>
#include <queue> // For implementing BFS
#include <stdexcept>
#include <sstream> // For converting a number to a string

using namespace std;

template<typename V>
class Graph
{
public:
// Construct an empty graph
Graph();

// Construct a graph from vertices in a vector and
//  edges in 2-D array
Graph(vector<V>& vertices, int edges[][2], int numberOfEdges);

// Construct a graph with vertices 0, 1, ..., n-1 and
// edges in 2-D array
Graph(int numberOfVertices, int edges[][2], int numberOfEdges);

// Construct a graph from vertices and edges objects
Graph(vector<V>& vertices, vector<Edge>& edges);

// Construct a graph with vertices 0, 1, ..., n-1 and
// edges in a vector
Graph(int numberOfVertices, vector<Edge>& edges);

// Return the number of vertices in the graph
int getSize() const;

// Return the degree for a specified vertex
int getDegree(int v) const;

// Return the vertex for the specified index
V getVertex(int index) const;

// Return the index for the specified vertex
int getIndex(V v) const;

// Return the vertices in the graph
vector<V> getVertices() const;

// Return the neighbors of vertex v
vector<int> getNeighbors(int v) const;

// Print the edges
void printEdges() const;

// Clear the graph
void clear();

// Adds a vertex to the graph

// Adds an edge from u to v to the graph

// Obtain a depth-first search tree
// To be discussed in Section 24.6
Tree dfs(int v) const;

// Starting bfs search from vertex v
// To be discussed in Section 24.7
Tree bfs(int v) const;

protected:
vector<V> vertices; // Store vertices
vector<vector<Edge*>> neighbors; // Adjacency edge lists
bool createEdge(Edge* e); // Add an edge

private:
// Create adjacency lists for each vertex from an edge array
int numberOfEdges);

// Create adjacency lists for each vertex from an Edge vector
vector<Edge>& edges);

// Recursive function for DFS search
void dfs(int v, vector<int>& parent,
vector<int>& searchOrders, vector<bool>& isVisited) const;
};

template<typename V>
Graph<V>::Graph()
{
}

template<typename V>
Graph<V>::Graph(vector<V>& vertices, int edges[][2],
int numberOfEdges)
{
for (unsigned i = 0; i < vertices.size(); i++)

}

template<typename V>
Graph<V>::Graph(int numberOfVertices, int edges[][2],
int numberOfEdges)
{
for (int i = 0; i < numberOfVertices; i++)
addVertex(i); // vertices is {0, 1, 2, ..., n-1}

}

template<typename V>
Graph<V>::Graph(vector<V>& vertices, vector<Edge>& edges)
{
for (unsigned i = 0; i < vertices.size(); i++)

}

template<typename V>
Graph<V>::Graph(int numberOfVertices, vector<Edge>& edges)
{
for (int i = 0; i < numberOfVertices; i++)
addVertex(i); // vertices is {0, 1, 2, ..., n-1}

}

template<typename V>
int edges[][2],  int numberOfEdges)
{
for (int i = 0; i < numberOfEdges; i++)
{
int u = edges[i][0];
int v = edges[i][1];
}
}

template<typename V>
vector<Edge>& edges)
{
for (unsigned i = 0; i < edges.size(); i++)
{
int u = edges[i].u;
int v = edges[i].v;
}
}

template<typename V>
int Graph<V>::getSize() const
{
return vertices.size();
}

template<typename V>
int Graph<V>::getDegree(int v) const
{
return neighbors[v].size();
}

template<typename V>
V Graph<V>::getVertex(int index) const
{
return vertices[index];
}

template<typename V>
int Graph<V>::getIndex(V v) const
{
for (unsigned i = 0; i < vertices.size(); i++)
{
if (vertices[i] == v)
return i;
}

return -1; // If vertex is not in the graph
}

template<typename V>
vector<V> Graph<V>::getVertices() const
{
return vertices;
}

template<typename V>
vector<int> Graph<V>::getNeighbors(int u) const
{
vector<int> result;
for (Edge* e: neighbors[u])
result.push_back(e->v);
return result;
}

template<typename V>
void Graph<V>::printEdges() const
{
for (unsigned u = 0; u < neighbors.size(); u++)
{
cout << "Vertex " << getVertex(u) << "(" << u << "): ";
for (Edge* e: neighbors[u])
{
cout << "(" << getVertex(e->u) << ", " << getVertex(e->v) << ") ";
}
cout << endl;
}
}

template<typename V>
{
// Use vector for 2-D array

// Initialize 2-D array for adjacency matrix
for (int i = 0; i < getSize(); i++)
{
}

for (unsigned i = 0; i < neighbors.size(); i++)
{
for (Edge* e: neighbors[i])
{
}
}

for (unsigned i = 0; i < adjacencyMatrix.size(); i++)
{
for (unsigned j = 0; j < adjacencyMatrix[i].size(); j++)
{
cout << adjacencyMatrix[i][j] << " ";
}

cout << endl;
}
}

template<typename V>
void Graph<V>::clear()
{
vertices.clear();
for (int i = 0; i < getSize(); i++)
for (Edge* e: neighbors[i])
delete e;
neighbors.clear();
}

template<typename V>
{
if (find(vertices.begin(), vertices.end(), v) == vertices.end())
{
vertices.push_back(v);
neighbors.push_back(vector<Edge*>(0));
return true;
}
else
{
return false;
}
}

template<typename V>
bool Graph<V>::createEdge(Edge* e)
{
if (e->u < 0 || e->u > getSize() - 1)
{
stringstream ss;
ss << e->u;
throw invalid_argument("No such edge: " + ss.str());
}

if (e->v < 0 || e->v > getSize() - 1)
{
stringstream ss;
ss << e->v;
throw invalid_argument("No such edge: " + ss.str());
}

vector<int> listOfNeighbors = getNeighbors(e->u);
if (find(listOfNeighbors.begin(), listOfNeighbors.end(), e->v)
== listOfNeighbors.end())
{
neighbors[e->u].push_back(e);
return true;
}
else
{
return false;
}
}

template<typename V>
{
return createEdge(new Edge(u, v));
}

template<typename V>
Tree Graph<V>::dfs(int u) const
{
vector<int> searchOrders;
vector<int> parent(vertices.size());
for (unsigned i = 0; i < vertices.size(); i++)
parent[i] = -1; // Initialize parent[i] to -1

// Mark visited vertices
vector<bool> isVisited(vertices.size());
for (unsigned i = 0; i < vertices.size(); i++)
{
isVisited[i] = false;
}

// Recursively search
dfs(u, parent, searchOrders, isVisited);

// Return a search tree
return Tree(u, parent, searchOrders);
}

template<typename V>
void Graph<V>::dfs(int u, vector<int>& parent,
vector<int>& searchOrders, vector<bool>& isVisited) const
{
// Store the visited vertex
searchOrders.push_back(u);
isVisited[u] = true; // Vertex v visited

for (Edge* e: neighbors[u])
{
if (!isVisited[e->v])
{
parent[e->v] = u; // The parent of vertex i is v
dfs(e->v, parent, searchOrders, isVisited); // Recursive search
}
}
}

template<typename V>
Tree Graph<V>::bfs(int v) const
{
vector<int> searchOrders;
vector<int> parent(vertices.size());
for (int i = 0; i < getSize(); i++)
parent[i] = -1; // Initialize parent[i] to -1

queue<int> queue; // Stores vertices to be visited
vector<bool> isVisited(getSize());
queue.push(v); // Enqueue v
isVisited[v] = true; // Mark it visited

while (!queue.empty())
{
int u = queue.front(); // Get from the front of the queue
queue.pop(); // remove the front element
searchOrders.push_back(u); // u searched
for (Edge* e: neighbors[u])
{
int w = e->v;
if (!isVisited[w])
{
queue.push(w); // Enqueue w
parent[w] = u; // The parent of w is u
isVisited[w] = true; // Mark it visited
}
}
}

return Tree(v, parent, searchOrders);
}

#endif
```