• 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/GD97_a
  • Description: Pajek network: Graph Drawing contest 1997
  • download as a MATLAB mat-file, file size: 3 KB. Use SJget(26) or SJget('Pajek/GD97_a') 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/GD97_a graph

    Matrix properties (click for a legend)  
    number of rows84
    number of columns84
    structural full rank?yes
    structural rank84
    numerical rank 80
    dimension of the numerical null space4
    numerical rank / min(size(A))0.95238
    Euclidean norm of A 3.9672
    calculated singular value # 800.042512
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 816.6172e-016
    gap in the singular values at the numerical rank:
    singular value # 80 / singular value # 81
    calculated condition number1.8304e+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
    kinddirected graph
    2D/3D problem?no

    Additional fieldssize and type
    coordfull 84-by-3


    Pajek network converted to sparse adjacency matrix for inclusion in UF sparse 
    matrix collection, Tim Davis.  For Pajek datasets, See V. Batagelj & A. Mrvar,

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))677 697
    Cholesky flop count6.9e+003 7.5e+003
    nnz(L+U), no partial pivoting1,270 1,310
    nnz(V) for QR, upper bound nnz(L) for LU985 998
    nnz(R) for QR, upper bound nnz(U) for LU1,609 1,624

    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.