• 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_a
  • Description: Pajek network: Graph Drawing contest 1996
  • download as a MATLAB mat-file, file size: 19 KB. Use SJget(22) or SJget('Pajek/GD96_a') in MATLAB.
  • download in Matrix Market format, file size: 12 KB.
  • download in Rutherford/Boeing format, file size: 12 KB.


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


    scc of Pajek/GD96_a

    Pajek/GD96_a graph

    Matrix properties (click for a legend)  
    number of rows1,096
    number of columns1,096
    structural full rank?no
    structural rank827
    numerical rank 827
    dimension of the numerical null space269
    numerical rank / min(size(A))0.75456
    Euclidean norm of A 12.455
    calculated singular value # 8270.4949
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 8282.8967e-015
    gap in the singular values at the numerical rank:
    singular value # 827 / singular value # 828
    calculated condition numberInf
    # of blocks from dmperm623
    # strongly connected comp.1,096
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

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

    Additional fieldssize and type
    nodenamefull 1096-by-1
    coordfull 1096-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'))6,547 8,003
    Cholesky flop count1.2e+005 1.8e+005
    nnz(L+U), no partial pivoting11,998 14,910
    nnz(V) for QR, upper bound nnz(L) for LU5,290 2,697
    nnz(R) for QR, upper bound nnz(U) for LU2,476 2,472

    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.