Самая простая реализация графа

#include <iostream>
#include <vector>
using namespace std;

struct node {
    int i = NULL;
    vector <int> edges;
    node* nextVertex;
    node(int n) {
        i = n;
        nextVertex = NULL;
    }
};

typedef node Node;

class Graph {
    Node* head;
    int N;
public:
    Graph(int t){
        this->N = t;
    }
    void addEdge(int, int, bool);
    void addVertex(int);
    node* existVertex(int);
    void print();
};

node* Graph::existVertex(int i) {
    node* cur = this->head;
    while (cur != NULL) {
        if (cur->i == i) {
            return cur;
            break;
        }
        cur = cur->nextVertex;
    }
    return 0;
}

void Graph::addEdge(int i, int j, bool status) {

    if (this->head == NULL) {
        this->head = new node(i);
        this->head->edges.push_back(j);
        node* cur = this->head;
        if (status == true) {
            cur->nextVertex = new node(j);
            cur->nextVertex->edges.push_back(i);
        }
    }
    else if (existVertex(i) != NULL) {
        node* cur = existVertex(i);
        cur->edges.push_back(j);
        if (existVertex(j) == NULL)
        cur->nextVertex = new node(j);
        if (status == true) {
            cur->nextVertex->edges.push_back(i);
        }
    }
    else {
        node* cur = this->head;
        while (cur->nextVertex != NULL) cur = cur->nextVertex;
        cur->nextVertex = new node(i); cur->edges.push_back(j);
        if (existVertex(j) == NULL)
        cur->nextVertex = new node(j);
        if (status == true) {
            cur->nextVertex->edges.push_back(i);
        }
    }
}

void Graph::addVertex(int i) {
    if (existVertex(i) == NULL) {
        node* cur = this->head;
        while (cur->nextVertex != NULL) cur = cur->nextVertex;
        cur->nextVertex = new node(i);
    }
}

void Graph::print() {
    node* cur = this->head;
    while (cur != NULL) {
        cout << cur->i << " -> ";
        if (cur->edges.size() == 1) {
            cout << *cur->edges.begin();
        }
        else {
            auto it = cur->edges.begin();
            auto end = cur->edges.end();
            while (it != end) {
                cout << *it << " ";
                it++;
            }
        }
        cur = cur->nextVertex;
        printf("\n");
    }
}

int main() {
    Graph G(10);
    G.addEdge(1, 7, true);
    G.addEdge(7, 5, true);
    G.addVertex(4);
    G.print();
    return 0;
}