• 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/GD01_A
  • Description: Pajek network: Graph Drawing contest 2001
  • download as a MATLAB mat-file, file size: 15 KB. Use SJget(528) or SJget('Pajek/GD01_A') in MATLAB.
  • download in Matrix Market format, file size: 7 KB.
  • download in Rutherford/Boeing format, file size: 7 KB.


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


    scc of Pajek/GD01_A

    Pajek/GD01_A graph

    Matrix properties (click for a legend)  
    number of rows953
    number of columns953
    structural full rank?no
    structural rank158
    numerical rank 155
    dimension of the numerical null space798
    numerical rank / min(size(A))0.16264
    Euclidean norm of A 6.4014
    calculated singular value # 1550.10285
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 1562.3692e-015
    gap in the singular values at the numerical rank:
    singular value # 155 / singular value # 156
    calculated condition numberInf
    # of blocks from dmperm61
    # strongly connected comp.945
    explicit zero entries0
    nonzero pattern symmetry 2%
    numeric value symmetry 2%
    Cholesky candidate?no
    positive definite?no

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

    Additional fieldssize and type
    nodenamefull 953-by-38
    coordfull 953-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'))2,903 3,153
    Cholesky flop count4.1e+004 5.4e+004
    nnz(L+U), no partial pivoting4,853 5,353
    nnz(V) for QR, upper bound nnz(L) for LU2,692 2,846
    nnz(R) for QR, upper bound nnz(U) for LU2,828 3,015

    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.