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) {
            // remove edge which introduced cycle
            removeEdge(from, to);
            throw new CycleDetectedException(

    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) {
            // remove edge which introduced cycle
            removeEdge(from, to);
            throw new CycleDetectedException(

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)) {
            List<String> cycle = visitCycle(graph, Collections.singleton(to), new HashMap<>(), new LinkedList<>());
            if (cycle != null) {
                // remove edge which introduced cycle