throw new GraphConflictResolutionException("graph with an entry, but not vertices do not exist");
        }

        if (graph.isEmptyEdges()) {
            return null; // no edges - nothing to worry about
        }

        final TreeSet<MetadataGraphVertex> vertices = graph.getVertices();

        try {
            // edge case - single vertex graph
            if (vertices.size() == 1) {