• 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/GD06_theory
  • Description: Pajek network: Graph Drawing contest 2006
  • download as a MATLAB mat-file, file size: 2 KB. Use SJget(19) or SJget('Pajek/GD06_theory') 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.


    Matrix properties (click for a legend)  
    number of rows101
    number of columns101
    structural full rank?no
    structural rank20
    numerical rank 20
    dimension of the numerical null space81
    numerical rank / min(size(A))0.19802
    Euclidean norm of A 6.7823
    calculated singular value # 204
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 213.3193e-015
    gap in the singular values at the numerical rank:
    singular value # 20 / singular value # 21
    calculated condition number1.5914e+050
    # of blocks from dmperm2
    # 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


    Pajek network converted to sparse adjacency matrix for inclusion in UF sparse 
    matrix collection, Tim Davis.  For Pajek datasets, See V. Batagelj & A. Mrvar,
     GD 2006 contest graph A: Theory                                              
     graph in Pajek format                                                        
     transformed by Vladimir Batagelj, July 10, 2006                              

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))336 336
    Cholesky flop count1.3e+003 1.3e+003
    nnz(L+U), no partial pivoting571 571
    nnz(V) for QR, upper bound nnz(L) for LU721 721
    nnz(R) for QR, upper bound nnz(U) for LU3,401 3,401

    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.