Implement a graph ADT by defining a class Graph with the ope

Implement a graph ADT by defining a class \"Graph\" with the operations below. Your ADT should accept either a directed or undirected graph. isDirect(): tests if the graph is a digraph. Returns Boolean value. adjacent(v, u): tests whether there is an edge from the vertex v to u. returns Boolean value. neighbors(v): returns the list of all vertices that are a destination of an edge from v. addVertex(v): adds the vertex v to the graph if it is not already in the graph, otherwise an error message to be thrown. removeVertex(v): removes vertex v from the graph, if it is there. When a vertex is removed, all edges associated with that vertex should be deleted as well. addEdge(v, u): adds the edge that starts from v and ends at u. addEdge(v, u, w): adds the edge that starts from v and ends at u with weight w. removeEdge(v, u): remove the edge that connects v and u. getWeight(v, u): returns the weight of the edge from v to u. setWeight(v, u): sets the weight of the edge from v to u. isEmpty(): check whether the graph is empty or not. isComplete(): checks whether the graph is complete or not. vertices():returns the list of vertices in the graph (i.e., array, vector, ..) edges(): returns the list of edges in the graph. degree(v): return the degree of vertex v. size(): returns the number of vertices in the graph. nEdges(): returns the number of edges in the graph. clear(): Reinitializes the graph to be empty, freeing any heap storage. vertexExists(v): tests whether a vertex is in the graph or not. Returns true or false. print(): displays the list of vertices, edges and their weights if the graph is weighted. Your ADT should contain at least these constructors: Graph(), creates a graph with zero vertices. Graph(n), creates a graph with n vertices. Graph(n, digraph), where digraph is a Boolean value if true means a directed graph.

Solution

Answer: See the code below

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using System;
using System.Collections.Generic;

namespace GraphADT
{
    //Graph ADT class
    abstract class Graph
    {
        //data members
        private int nV; //number of vertices
        private int nE; //number of edges
        private int[,] adjMatrix; //adjaceny matrix for graph
        private bool directedGraph; //flag for graph being directed graph

        //constructors
        //creates a graph with zero vertices
        public Graph()
        {
            nV = 0;
            nE = 0;
            directedGraph = false;
        }
        //creates a graph with n vertices
        public Graph(int n)
        {
            nV = n;
            nE = 0;
            adjMatrix = new int[n,n];
            directedGraph = false;
        }
        //creates a digraph with n vertices
        public Graph(int n, bool digraph)
        {
            nV = n;
            nE = 0;
            adjMatrix = new int[n, n];
            directedGraph = digraph;
        }

        //methods
        //tests is the graph is a diagraph.
        public abstract bool isDirect();
        //tests whether there is an edge from vertex v to u
        public abstract bool adjacent(int u, int v);
        //returns the list of all vertices that are a destination of an edge from v.
        public abstract List<int> neighbours(int v);
        //adds the vertex v to the graph, if not already in graph, otherwise an error message is thrown.
        public abstract void addVertex(int v);
        //removes vertex v from the graph, if it is there. When a vertex is removed, all edges associated
        //with that vertex are also removed.
        public abstract void removeVertex(int v);
        //add the edge that starts from v and ends at u.
        public abstract void addEdge(int v, int u);
        //add the edge that starts from v and ends at u with weight w.
        public abstract void addEdge(int v, int u, int w);
        //returns the weight of edge from v to u.
        public abstract void getWeight(int v, int u);
        //sets the weight of edge from v to u.
        public abstract void setWeight(int v, int u);
        //checks whether graph is empty or not
        public abstract bool isEmpty();
        //checks whether the graph is complete or not
        public abstract bool isComplete();
        //returns the list of vertices in graph
        public abstract List<int> vertices();
        //returns the list of edges in the graph
        public abstract int[][] edges();
        //returns the degree of vertex v
        public abstract int degree(int v);
        //returns the number of vertices in graph
        public abstract int size();
        //returns the number of edges in graph
        public abstract int nEdges();
        //Reinitializes the graph to be empty, freeing any heap storage
        public abstract void clear();
        //tests whether a vertex is in the graph or not
        public abstract bool vertexExists(int v);
        //displays the list of vertices, edges and their weights, if the graph is weighted
        public abstract void print();
    }

}