Code for https://stackoverflow.com/q/77002310/16582

main.cpp

#include <string>
#include <fstream>
#include <sstream>
#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>

#include "GraphTheory.h"

#include <iostream>

void readDot(std::istringstream &input, raven::graph::sGraphData &gd)
{
    gd.g.clear();
    gd.g.directed();

    std::string a;
    while (getline(input, a, ';'))
    {
        int p = a.find("->");
        if (p != -1)
        {
            gd.g.add(a.substr(0, p),
                     a.substr(p + 2));
        }
    }
}

void bfs(
    raven::graph::sGraphData &gd)
{
    // queue of visited vertices with unsearched children
    std::queue<int> Q;

    // track nodes that have been visited
    // prevent getting caught going around and around a cycle
    std::vector<bool> visited(gd.g.vertexCount(), false);

    // get vertex indices from user names
    int start = gd.g.find(gd.startName);

    // start at start

    int v = start;
    std::cout << gd.g.userName(v) << " ";
    Q.push(v);
    visited[v] = true;

    // loop while the queue is not empty
    while (!Q.empty())
    {
        // get current vertex from front of queue
        v = Q.front();
        Q.pop();

        // loop over vertices reachable from current vertex
        for (int u : gd.g.adjacentOut(v))
        {
            if (!visited[u])
            {
                // visit to a new node
                std::cout << gd.g.userName(u) << " ";

                // add to queue and mark visited
                Q.push(u);
                visited[u] = true;
            }
        }
    }

    std::cout << "\n";
}

int main()
{
    std::istringstream input(
        "digraph{"
        "0;1;2;3;4;5;6;7;8;9;"
        "0->1;1->2;2->3;2->6;3->4;4->5;5->8;6->7;6->5;7->8;8->9;"
        "}");
    const std::string start_index = "6";

    raven::graph::sGraphData gd;
    gd.startName = "6";

    readDot(input, gd);

    bfs(gd);
}