• 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/GD99_b
  • Description: Pajek network: Graph Drawing contest 1999
  • download as a MATLAB mat-file, file size: 3 KB. Use SJget(32) or SJget('Pajek/GD99_b') 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/GD99_b graph

    Matrix properties (click for a legend)  
    number of rows64
    number of columns64
    structural full rank?yes
    structural rank64
    numerical rank 45
    dimension of the numerical null space19
    numerical rank / min(size(A))0.70313
    Euclidean norm of A 3.9825
    calculated singular value # 450.33018
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 461.463e-015
    gap in the singular values at the numerical rank:
    singular value # 45 / singular value # 46
    calculated condition number9.3449e+016
    # 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 multigraph
    2D/3D problem?no

    Additional fieldssize and type
    nodenamefull 64-by-5
    coordfull 64-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'))461 478
    Cholesky flop count4.1e+003 4.4e+003
    nnz(L+U), no partial pivoting858 892
    nnz(V) for QR, upper bound nnz(L) for LU573 558
    nnz(R) for QR, upper bound nnz(U) for LU980 947

    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.