def is_connected(T, directed=True):
    r"""Check connectivity of the transition matrix.

    Return true, if the input matrix is completely connected,
    effectively checking if the number of connected components equals one.

    Parameters
    ----------
    T : scipy.sparse matrix
        Transition matrix
    directed : bool, optional
       Whether to compute connected components for a directed  or
       undirected graph. Default is True.

    Returns
    -------
    connected : boolean, returning true only if T is connected.


    """
    nc = connected_components(T, directed=directed, connection='strong', \
                              return_labels=False)
    return nc == 1