// v1-->v2
        graph.addEdge(v1, v2, new MetadataGraphEdge("1.1", true, null, null, 2, 1));
        graph.addEdge(v1, v2, new MetadataGraphEdge("1.2", true, null, null, 2, 2));

        // v1-->v3
        graph.addEdge(v1, v3, new MetadataGraphEdge("1.1", true, null, null, 2, 1));
        graph.addEdge(v1, v3, new MetadataGraphEdge("1.2", true, null, null, 4, 2));

        // v3-->v4

        // v1-->v2
        graph.addEdge(v1, v2, new MetadataGraphEdge("1.1", true, null, null, 2, 1));
        graph.addEdge(v1, v2, new MetadataGraphEdge("1.2", true, null, null, 2, 2));

        // v1-->v3
        graph.addEdge(v1, v3, new MetadataGraphEdge("1.1", true, null, null, 2, 1));
        graph.addEdge(v1, v3, new MetadataGraphEdge("1.2", true, null, null, 4, 2));

        // v3-->v4

                    // gathered with problem collector
                }
                return null;
            }
        };
    }

    private boolean addEdge(Path from, Path p, DefaultModelProblemCollector problems) {
        try {
            dag.addEdge(from.toString(), p.toString());
            return true;
        } catch (Graph.CycleDetectedException e) {
            problems.add(new DefaultModelProblem(

import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Set;

class Graph {

    final Map<String, Set<String>> graph = new LinkedHashMap<>();

    synchronized void addEdge(String from, String to) throws CycleDetectedException {
        if (graph.computeIfAbsent(from, l -> new HashSet<>()).add(to)) {

    public Collection<Vertex> getVertices() {
        return vertices.values();
    }

    Vertex addVertex(String label) {
        return vertices.computeIfAbsent(label, Vertex::new);
    }

    void addEdge(Vertex from, Vertex to) throws CycleDetectedException {
        from.children.add(to);
        to.parents.add(from);
        List<String> cycle = findCycle(to);
        if (cycle != null) {