• 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/GD02_a
  • Description: Pajek network: Graph Drawing contest 2002
  • download as a MATLAB mat-file, file size: 2 KB. Use SJget(16) or SJget('Pajek/GD02_a') in MATLAB.
  • download in Matrix Market format, file size: 1 KB.
  • download in Rutherford/Boeing format, file size: 1 KB.

    Pajek/GD02_a

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

    Pajek/GD02_a

    scc of Pajek/GD02_a

    Pajek/GD02_a graph

    Matrix properties (click for a legend)  
    number of rows23
    number of columns23
    structural full rank?no
    structural rank19
    numerical rank 18
    dimension of the numerical null space5
    numerical rank / min(size(A))0.78261
    Euclidean norm of A 5.8265
    calculated singular value # 180.24916
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.0428e-014
    calculated singular value # 193.6366e-016
    gap in the singular values at the numerical rank:
    singular value # 18 / singular value # 19
    6.8515e+014
    calculated condition numberInf
    condestInf
    nonzeros87
    # of blocks from dmperm10
    # strongly connected comp.3
    explicit zero entries0
    nonzero pattern symmetry 64%
    numeric value symmetry 64%
    typebinary
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorGraph Drawing Contest
    editorV. Batagelj
    date2002
    kinddirected graph
    2D/3D problem?no
    SJid16
    UFid1,481

    Additional fieldssize and type
    nodenamefull 23-by-27
    coordfull 23-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 0.5, and have been removed.  This graph has 2D coordinates.                
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))94 93
    Cholesky flop count4.5e+002 4.4e+002
    nnz(L+U), no partial pivoting165 163
    nnz(V) for QR, upper bound nnz(L) for LU71 131
    nnz(R) for QR, upper bound nnz(U) for LU208 238

    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.