• 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_c
  • Description: Pajek network: Graph Drawing contest 1998
  • download as a MATLAB mat-file, file size: 4 KB. Use SJget(31) or SJget('Pajek/GD98_c') in MATLAB.
  • download in Matrix Market format, file size: 2 KB.
  • download in Rutherford/Boeing format, file size: 2 KB.


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


    Pajek/GD98_c graph

    Matrix properties (click for a legend)  
    number of rows112
    number of columns112
    structural full rank?yes
    structural rank112
    numerical rank 100
    dimension of the numerical null space12
    numerical rank / min(size(A))0.89286
    Euclidean norm of A 3
    calculated singular value # 1000.30611
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 1018.8102e-016
    gap in the singular values at the numerical rank:
    singular value # 100 / singular value # 101
    calculated condition number2.5363e+017
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?no

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

    Additional fieldssize and type
    coordfull 112-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 0.5, and have been removed.  This graph has 2D coordinates.                

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))967 979
    Cholesky flop count1.4e+004 1.4e+004
    nnz(L+U), no partial pivoting1,822 1,846
    nnz(V) for QR, upper bound nnz(L) for LU1,306 1,081
    nnz(R) for QR, upper bound nnz(U) for LU2,056 1,877

    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.