• 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_c
  • Description: Pajek network: Graph Drawing contest 1996
  • download as a MATLAB mat-file, file size: 2 KB. Use SJget(24) or SJget('Pajek/GD96_c') in MATLAB.
  • download in Matrix Market format, file size: 1 KB.
  • download in Rutherford/Boeing format, file size: 1 KB.


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


    Pajek/GD96_c graph

    Matrix properties (click for a legend)  
    number of rows65
    number of columns65
    structural full rank?no
    structural rank64
    numerical rank 63
    dimension of the numerical null space2
    numerical rank / min(size(A))0.96923
    Euclidean norm of A 4.1411
    calculated singular value # 630.11734
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 644.5563e-016
    gap in the singular values at the numerical rank:
    singular value # 63 / singular value # 64
    calculated condition number4.1421e+016
    # of blocks from dmperm3
    # strongly connected comp.1
    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
    nodenamefull 65-by-1
    coordfull 65-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'))341 367
    Cholesky flop count2.0e+003 2.4e+003
    nnz(L+U), no partial pivoting617 669
    nnz(V) for QR, upper bound nnz(L) for LU366 422
    nnz(R) for QR, upper bound nnz(U) for LU623 653

    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.