• SJSU Singular Matrix Database
  • Matrix group: Pajek
  • Click here for a description of the Pajek group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups


  • Matrix: Pajek/GD96_d
  • Description: Pajek network: Graph Drawing contest 1996
  • download as a MATLAB mat-file, file size: 7 KB. Use SJget(25) or SJget('Pajek/GD96_d') in MATLAB.
  • download in Matrix Market format, file size: 4 KB.
  • download in Rutherford/Boeing format, file size: 4 KB.

    Pajek/GD96_d

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

    Pajek/GD96_d

    scc of Pajek/GD96_d

    Pajek/GD96_d graph

    Matrix properties (click for a legend)  
    number of rows180
    number of columns180
    structural full rank?no
    structural rank73
    numerical rank 73
    dimension of the numerical null space107
    numerical rank / min(size(A))0.40556
    Euclidean norm of A 4.899
    calculated singular value # 730.4658
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.5987e-013
    calculated singular value # 746.0421e-015
    gap in the singular values at the numerical rank:
    singular value # 73 / singular value # 74
    7.7093e+013
    calculated condition numberInf
    condestInf
    nonzeros229
    # of blocks from dmperm45
    # strongly connected comp.168
    explicit zero entries0
    nonzero pattern symmetry 1%
    numeric value symmetry 1%
    typebinary
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorGraph Drawing Contest
    editorV. Batagelj
    date1996
    kinddirected graph
    2D/3D problem?no
    SJid25
    UFid1,491

    Additional fieldssize and type
    nodenamefull 180-by-40
    coordfull 180-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/.                                
    ------------------------------------------------------------------------------
    The original problem had 3D xyz coordinates, but all values of z were equal   
    to 0, and have been removed.  This graph has 2D coordinates.                  
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))464 466
    Cholesky flop count1.4e+003 1.4e+003
    nnz(L+U), no partial pivoting748 752
    nnz(V) for QR, upper bound nnz(L) for LU359 301
    nnz(R) for QR, upper bound nnz(U) for LU1,221 1,221

    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.