ó ,ľ[c@sźdZddlZddlmZdjddddgƒZd d d gZed ƒdd d„ƒZ ed ƒdd d„ƒZ edƒedƒdd ddd„ƒƒZ d„Z dS(sLaplacian matrix of graphs. i˙˙˙˙N(tnot_implemented_fors s%Aric Hagberg sPieter Swart (swart@lanl.gov)s Dan Schult (dschult@colgate.edu)s3Alejandro Weinstein tlaplacian_matrixtnormalized_laplacian_matrixtdirected_laplacian_matrixtdirectedtweightc Cs›ddl}|dkr't|ƒ}ntj|d|d|ddƒ}|j\}}|jddƒ}|jj|j ƒd g||ddƒ}||S( sEReturn the Laplacian matrix of G. The graph Laplacian is the matrix L = D - A, where A is the adjacency matrix and D is the diagonal matrix of node degrees. Parameters ---------- G : graph A NetworkX graph nodelist : list, optional The rows and columns are ordered according to the nodes in nodelist. If nodelist is None, then the ordering is produced by G.nodes(). weight : string or None, optional (default='weight') The edge data key used to compute each value in the matrix. If None, then each edge has weight 1. Returns ------- L : SciPy sparse matrix The Laplacian matrix of G. Notes ----- For MultiGraph/MultiDiGraph, the edges weights are summed. See Also -------- to_numpy_matrix normalized_laplacian_matrix i˙˙˙˙NtnodelistRtformattcsrtaxisii( t scipy.sparsetNonetlisttnxtto_scipy_sparse_matrixtshapetsumtsparsetspdiagstflatten( tGRRtscipytAtntmtdiagstD((s>lib/python2.7/site-packages/networkx/linalg/laplacianmatrix.pyRs"   *c Cs"ddl}ddl}|dkr3t|ƒ}ntj|d|d|ddƒ}|j\}}|jddƒjƒ}|j j |d g||ddƒ}||} |j d d ƒd |j |ƒ} WdQXd | |j | ƒ<|j j | d g||ddƒ} | j| j| ƒƒS( sRReturn the normalized Laplacian matrix of G. The normalized graph Laplacian is the matrix .. math:: N = D^{-1/2} L D^{-1/2} where `L` is the graph Laplacian and `D` is the diagonal matrix of node degrees. Parameters ---------- G : graph A NetworkX graph nodelist : list, optional The rows and columns are ordered according to the nodes in nodelist. If nodelist is None, then the ordering is produced by G.nodes(). weight : string or None, optional (default='weight') The edge data key used to compute each value in the matrix. If None, then each edge has weight 1. Returns ------- N : NumPy matrix The normalized Laplacian matrix of G. Notes ----- For MultiGraph/MultiDiGraph, the edges weights are summed. See to_numpy_matrix for other options. If the Graph contains selfloops, D is defined as diag(sum(A,1)), where A is the adjacency matrix [2]_. See Also -------- laplacian_matrix References ---------- .. [1] Fan Chung-Graham, Spectral Graph Theory, CBMS Regional Conference Series in Mathematics, Number 92, 1997. .. [2] Steve Butler, Interlacing For Weighted Graphs Using The Normalized Laplacian, Electronic Journal of Linear Algebra, Volume 16, pp. 90-98, March 2007. i˙˙˙˙NRRRRR iitdividetignoregđ?(RR R R R RRRRRRterrstatetsqrttisinftdot( RRRRRRRRRtLt diags_sqrttDH((s>lib/python2.7/site-packages/networkx/linalg/laplacianmatrix.pyRAs3    $ $t undirectedt multigraphgffffffî?cCs‰ddl}ddlm}m}m}|dkrmtj|ƒrdtj|ƒr[d}qjd}qmd}ntj |d|d|d t ƒ} | j \} } |dkr|d |j | j d d ƒjƒd g| | ƒ} |dkrö| | } qß|| ƒ}|| | d} nČ|dkrĐd |ko:d knsQtjdƒ‚n| jƒ} |j| j d d ƒd kƒ}x |d D]}d | | |lib/python2.7/site-packages/networkx/linalg/laplacianmatrix.pyR‰sDC       4     !6cCs:ddlm}yddl}Wn|dƒ‚nXdS(Ni˙˙˙˙(tSkipTestsNumPy not available(tnoseRHtnumpy(tmoduleRHRJ((s>lib/python2.7/site-packages/networkx/linalg/laplacianmatrix.pyt setup_moduleýs ( t__doc__tnetworkxR tnetworkx.utilsRtjoint __author__t__all__R RRRRL(((s>lib/python2.7/site-packages/networkx/linalg/laplacianmatrix.pyts$     , G  q