cluster_from->Merge(cluster_to);
    // Update `cycle_graph_`'s ID.
    cluster_from->set_cycles_graph_node_id(optional_merged_node.value());

    // Merge the UnionFind<Cluster*>.
    cluster_for_node_[from].Merge(&cluster_for_node_[to]);

    return true;
  }

  string EdgeContractionFailureMsg(Cluster* from, Cluster* to,
                                   absl::string_view reason) {