def METHOD_NAME(G):
    """Returns True if the graph is connected, False otherwise.
    Parameters
    ----------
    G : NetworkX Graph
       An undirected graph.
    Returns
    -------
    connected : bool
      True if the graph is connected, false otherwise.
    Raises
    ------
    NetworkXNotImplemented
        If G is directed.
    Examples
    --------
    >>> G = nx.path_graph(4)
    >>> print(nx.is_connected(G))
    True
    See Also
    --------
    is_strongly_connected
    is_weakly_connected
    is_semiconnected
    is_biconnected
    connected_components
    Notes
    -----
    For undirected graphs only.
    """
    if len(G) == 0:
        raise nx.NetworkXPointlessConcept(
            "Connectivity is undefined ", "for the null graph."
        )
    return sum(1 for node in _plain_bfs(G, arbitrary_element(G))) == len(G)