Module « scipy.sparse.csgraph »

Fonction laplacian - module scipy.sparse.csgraph

Signature de la fonction laplacian

def laplacian(csgraph, normed=False, return_diag=False, use_out_degree=False) 

Description

laplacian.__doc__

    Return the Laplacian matrix of a directed graph.

    Parameters
    ----------
    csgraph : array_like or sparse matrix, 2 dimensions
        compressed-sparse graph, with shape (N, N).
    normed : bool, optional
        If True, then compute symmetric normalized Laplacian.
    return_diag : bool, optional
        If True, then also return an array related to vertex degrees.
    use_out_degree : bool, optional
        If True, then use out-degree instead of in-degree.
        This distinction matters only if the graph is asymmetric.
        Default: False.

    Returns
    -------
    lap : ndarray or sparse matrix
        The N x N laplacian matrix of csgraph. It will be a NumPy array (dense)
        if the input was dense, or a sparse matrix otherwise.
    diag : ndarray, optional
        The length-N diagonal of the Laplacian matrix.
        For the normalized Laplacian, this is the array of square roots
        of vertex degrees or 1 if the degree is zero.

    Notes
    -----
    The Laplacian matrix of a graph is sometimes referred to as the
    "Kirchoff matrix" or the "admittance matrix", and is useful in many
    parts of spectral graph theory. In particular, the eigen-decomposition
    of the laplacian matrix can give insight into many properties of the graph.

    Examples
    --------
    >>> from scipy.sparse import csgraph
    >>> G = np.arange(5) * np.arange(5)[:, np.newaxis]
    >>> G
    array([[ 0,  0,  0,  0,  0],
           [ 0,  1,  2,  3,  4],
           [ 0,  2,  4,  6,  8],
           [ 0,  3,  6,  9, 12],
           [ 0,  4,  8, 12, 16]])
    >>> csgraph.laplacian(G, normed=False)
    array([[  0,   0,   0,   0,   0],
           [  0,   9,  -2,  -3,  -4],
           [  0,  -2,  16,  -6,  -8],
           [  0,  -3,  -6,  21, -12],
           [  0,  -4,  -8, -12,  24]])