• 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/GD98_b
  • Description: Pajek network: Graph Drawing contest 1998
  • download as a MATLAB mat-file, file size: 4 KB. Use SJget(30) or SJget('Pajek/GD98_b') in MATLAB.
  • download in Matrix Market format, file size: 2 KB.
  • download in Rutherford/Boeing format, file size: 2 KB.

    Pajek/GD98_b

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

    Pajek/GD98_b

    scc of Pajek/GD98_b

    Pajek/GD98_b graph

    Matrix properties (click for a legend)  
    number of rows121
    number of columns121
    structural full rank?no
    structural rank87
    numerical rank 87
    dimension of the numerical null space34
    numerical rank / min(size(A))0.71901
    Euclidean norm of A 2.8497
    calculated singular value # 870.51764
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    5.3735e-014
    calculated singular value # 885.9578e-016
    gap in the singular values at the numerical rank:
    singular value # 87 / singular value # 88
    8.6884e+014
    calculated condition number6.9474e+033
    condestInf
    nonzeros207
    # of blocks from dmperm23
    # strongly connected comp.12
    explicit zero entries0
    nonzero pattern symmetry 72%
    numeric value symmetry 72%
    typebinary
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorGraph Drawing Contest
    editorV. Batagelj
    date1998
    kinddirected graph
    2D/3D problem?no
    SJid30
    UFid1,496

    Additional fieldssize and type
    nodenamefull 121-by-6
    coordfull 121-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 0.5241, and have been removed.  This graph has 2D coordinates.             
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))274 291
    Cholesky flop count6.5e+002 7.7e+002
    nnz(L+U), no partial pivoting427 461
    nnz(V) for QR, upper bound nnz(L) for LU247 190
    nnz(R) for QR, upper bound nnz(U) for LU284 284

    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.