Сортировка в графике c ++

Question

Мне нужно знать, есть ли способ сделать сортировку по количеству ребер в списке узлов графа. Вот что я пробовал, но из-за направлений памяти края не правильные. Спасибо!

Пример: CHAMANISMO-> 1-> PROPICIACION

PROPICIACION-> 2-> SACERDOTE

Финальная версия: PROPICIACION-> 2-> SACERDOTE

CHAMANISMO-> 1-> CHAMANISMO, но оно должно быть CHAMANISMO-> 1-> PROPICIACION

код:

#ifndef GRAPH_H_
#define GRAPH_H_

#include <string>
#include <iostream>

using namespace std;

class Edge;

class NodeGraph{
    string word;//nombre del vertice o nodo
    NodeGraph *next;
    Edge *ady;//puntero hacia la primera arista del nodo
    friend class Graph;
    public:
        NodeGraph(){
            word = "";
            next = NULL;
            ady = NULL;
        }
};

//es cada arista
class Edge{
    NodeGraph *ady;//puntero al nodo de llegada
    Edge *next;
    int timeNodeGraphs; //es el peso
    friend class Graph;
    public:
        Edge(){
            ady = NULL;
            next = NULL;
            timeNodeGraphs = 0;
        }
};

//es el grafo principal
class Graph{
    NodeGraph *first = new NodeGraph();
    //NodeGraph *last = new NodeGraph(); /////////////////agregado
    public:
        Graph(){
            first = NULL;
            //last = NULL; /////////////////agregado
        }
        void insert_NodeGraph(string);
        void link_Edge(NodeGraph*, NodeGraph*);
        bool search_NodeGraph(string);
        NodeGraph* get_NodeGraph(string); //regresa la direccion del vertice
        void node_Sort();
        Edge* get_Edges(NodeGraph*);
};

//Inserta un nodo
void Graph::insert_NodeGraph(string words){
    NodeGraph *nuevo = new NodeGraph(); //crea el nodo a insertar
    nuevo->word = words;
    nuevo->next = NULL;
    nuevo->ady=NULL;

    if (search_NodeGraph(words) or words == "") {return;}
    if(first==NULL){
        first = nuevo;
    }
    else{
        NodeGraph *aux = first; //auxiliar
        while(aux->next!=NULL){ //recorre hasta llegar al ultimo
            aux = aux->next;
          }
        aux->next = nuevo; //crea el ultimo nodo
      }
 }

//realiza las relaciones
void Graph::link_Edge(NodeGraph *origin, NodeGraph *desti){
    Edge *newEdge = new Edge(); //crea un nuevo arco
    newEdge->timeNodeGraphs = 1;
    newEdge->next = NULL;
    newEdge->ady = NULL;
    Edge *aux = origin->ady; //auxiliar

    if(origin->ady == NULL){ //en caso de ser nulo el primer arco
        origin->ady = newEdge;
        newEdge->ady = desti;
    }
    else if(aux->ady->word == desti->word){
        aux->timeNodeGraphs = aux->timeNodeGraphs + 1;
    }
    else{
        while(aux->next != NULL){ //recorre todos los arcos
            if(aux->ady->word == desti->word){ //en caso que el arco ya exista
                aux->timeNodeGraphs = aux->timeNodeGraphs + 1; //se le suma al valor
                return;
            }
            aux = aux->next;
        }
        if(aux->ady->word == desti->word){ //en caso que el arco ya exista
            aux->timeNodeGraphs = aux->timeNodeGraphs + 1; //se le suma al valor
            return;
        }
        aux->next = newEdge; //asigna el nuevo arco
        newEdge->ady = desti; //asigna el destino
    }
}

//cuenta los arcos que hay y suma su peso
int Graph::Edge_number(NodeGraph* word){
    int number_Edges = 0;
    Edge* first = word->ady;
    while (first != NULL){
        number_Edges = first->timeNodeGraphs + number_Edges;
        first = first->next;
    }
    return number_Edges;
}

//Hace un sort de los nodos
void Graph::node_Sort(){
    NodeGraph* aux = first;
    NodeGraph* nextN;
    NodeGraph* aux2;
    Edge* adyE;
    string words;

    while(aux->next != NULL){
       nextN = aux->next;
       while(nextN != NULL){
           if(Edge_number(aux) < Edge_number(nextN) && aux->next != nextN){
                adyE = nextN->ady;
                aux2 = nextN;
                words = nextN->word;
                nextN->word = aux->word;
                nextN->ady = aux->ady;
                nextN = aux;
                aux->word = words;
                aux->ady = adyE;
                aux = aux2;
           }
           nextN = nextN->next;
       }
       aux = aux->next;
    }
}

#endif /* GRAPH_H_ */