• SJSU Singular Matrix Database
  • Matrix group: Pajek
  • Click here for a description of the Pajek group.
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  • Matrix: Pajek/GD97_b
  • Description: Pajek network: Graph Drawing contest 1997
  • download as a MATLAB mat-file, file size: 5 KB. Use SJget(27) or SJget('Pajek/GD97_b') in MATLAB.
  • download in Matrix Market format, file size: 3 KB.
  • download in Rutherford/Boeing format, file size: 3 KB.

    Pajek/GD97_b

    Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

    Pajek/GD97_b

    scc of Pajek/GD97_b

    Pajek/GD97_b graph

    Matrix properties (click for a legend)  
    number of rows47
    number of columns47
    structural full rank?no
    structural rank44
    numerical rank 44
    dimension of the numerical null space3
    numerical rank / min(size(A))0.93617
    Euclidean norm of A 2841.1
    calculated singular value # 440.00053395
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.1373e-011
    calculated singular value # 451.4045e-014
    gap in the singular values at the numerical rank:
    singular value # 44 / singular value # 45
    3.8017e+010
    calculated condition numberInf
    condestInf
    nonzeros264
    # of blocks from dmperm24
    # strongly connected comp.2
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typereal
    structuresymmetric
    Cholesky candidate?yes
    positive definite?no

    authorGraph Drawing Contest
    editorV. Batagelj
    date1997
    kindundirected weighted graph
    2D/3D problem?no
    SJid27
    UFid1,493

    Additional fieldssize and type
    nodenamefull 47-by-30
    coordfull 47-by-2

    Notes:

    ------------------------------------------------------------------------------
    Pajek network converted to sparse adjacency matrix for inclusion in UF sparse 
    matrix collection, Tim Davis.  For Pajek datasets, See V. Batagelj & A. Mrvar,
    http://vlado.fmf.uni-lj.si/pub/networks/data/.                                
    ------------------------------------------------------------------------------
    Regarding conversion for UF sparse matrix collection: in the original data    
    every edge appears exactly twice, with the same edge weight.  It could be a   
    multigraph, but it looks more like a graph.  The duplicate edges are removed  
    in this version.  You can always add them back in yourself; just look at 2*A. 
    ------------------------------------------------------------------------------
    The original problem had 3D xyz coordinates, but all values of z were equal   
    to 0.5, and have been removed.  This graph has 2D coordinates.                
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))211 220
    Cholesky flop count1.0e+003 1.1e+003
    nnz(L+U), no partial pivoting375 393
    nnz(V) for QR, upper bound nnz(L) for LU401 274
    nnz(R) for QR, upper bound nnz(U) for LU719 770

    Maintained by Leslie Foster, last updated 24-Apr-2009.

    Entries 5 through 14 in the table of matrix properties and the singular
    value plot were created using SJsingular code. The other plots
    and statistics are produced using utilities from the SuiteSparse package.
    Matrix color plot pictures by cspy, a MATLAB function in the CSparse package.