Find minimum weighted path in a vector of tuples representing a graph

Question

I am still new to graphs and am building a weighted directed graph for a school project. I was able to complete all the functions except the one that find the minimum weighted path from a node to another. I am able to find a path, but don't know how I would store all the paths then get the minimum weighted one. My graph is represented by a vector .

I have created a helper function that gives me a path from the source to the destination and a function that finds the weight of the path. They both work but I can't get the one that find the path to find all the paths instead of the first one it finds.

int WeightedDigraph::Myhelp(int to) const{
    for (mytup::const_iterator k = adjList.begin(); k != adjList.end(); ++k) {
        if(get<1>(*k) == to){ //destination
                return get<0>(*k); //source
        }
    }
    return 10000;
}

list<int> WeightedDigraph::FindMinimumWeightedPath(int from, int to) const {
    list<int> minpath;
    minpath.push_front(to);
    int src = Myhelp(to);
    while(src != from){
        minpath.push_front(src);
            src = Myhelp(src);
    }
    return minpath;
}

This code returns a list for "a" path from "from" to "to". Instead, I want it to return the one with the least weight. I have to function getPathWeight(const list& path ) already setup to find the weight of each path and compare them but how can I get all paths in one place?

Update for minimum, working example with includes:

Main.cpp

    #include "WeightedDigraph.h"
#include <iostream>
#include <string>
#include <list>
using namespace std;

int main(int argc, char* argv[])
{

    if(argc != 4) {
        cerr << "Incorrect number of command line arguments." << endl;
        cerr << "Usage: " << argv[0] << " <filename> <start vertex> <dest vertex>" << endl;
        exit(EXIT_FAILURE);
    }

    WeightedDigraph graph(argv[1]);

    cout << "The graph has " << graph.GetOrder() << " vertices and " << graph.GetSize() << " arcs" << endl;

    int source = atoi(argv[2]);
    int dest = atoi(argv[3]);

    if (graph.DoesPathExist(source, dest)) {
        list<int> path = graph.FindMinimumWeightedPath(source, dest);
        //then the path will be used for other functions
    return 0;
}

WeightedDiagraph.cpp:

#include "WeightedDigraph.h"
#include <iostream>
#include <fstream>
#include <sstream>
#include <limits>
#include<list>

using namespace std;


void WeightedDigraph::InsertArc(int from, int to, double weight) {
    tuple<int, int, double> newtup (from, to, weight); 
    adjList.push_back(newtup);
}

double WeightedDigraph::GetPathWeight(const list<int> & path) const {
    //working
}

//other functions that are not needed for my question

WeightedDiagraph.h:

#ifndef WeightedDigraph_H
#define WeightedDigraph_H

#include<list>
#include<string>
#include<vector>
#include<tuple>

using namespace std;

typedef vector<tuple<int,int,double>> mytup;

class WeightedDigraph {
public:
    mytup adjList;
    //all methods

private:
    int numVertices;
    int numArcs;

    int from;
    int to;
    double weight;

}