• 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/GD95_a
  • Description: Pajek network: Graph Drawing contest 1995
  • download as a MATLAB mat-file, file size: 2 KB. Use SJget(20) or SJget('Pajek/GD95_a') in MATLAB.
  • download in Matrix Market format, file size: 1 KB.
  • download in Rutherford/Boeing format, file size: 1 KB.


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


    scc of Pajek/GD95_a

    Pajek/GD95_a graph

    Matrix properties (click for a legend)  
    number of rows36
    number of columns36
    structural full rank?no
    structural rank32
    numerical rank 31
    dimension of the numerical null space5
    numerical rank / min(size(A))0.86111
    Euclidean norm of A 3.559
    calculated singular value # 310.44504
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 322.1046e-016
    gap in the singular values at the numerical rank:
    singular value # 31 / singular value # 32
    calculated condition number1.3288e+018
    # of blocks from dmperm23
    # strongly connected comp.4
    explicit zero entries0
    nonzero pattern symmetry 4%
    numeric value symmetry 4%
    Cholesky candidate?no
    positive definite?no

    authorGraph Drawing Contest
    editorV. Batagelj
    kinddirected graph
    2D/3D problem?no

    Additional fieldssize and type
    nodenamefull 36-by-31
    coordfull 36-by-2


    Pajek network converted to sparse adjacency matrix for inclusion in UF sparse 
    matrix collection, Tim Davis.  For Pajek datasets, See V. Batagelj & A. Mrvar,
    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'))118 138
    Cholesky flop count4.1e+002 6.0e+002
    nnz(L+U), no partial pivoting200 240
    nnz(V) for QR, upper bound nnz(L) for LU47 49
    nnz(R) for QR, upper bound nnz(U) for LU69 70

    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.