• 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/football
  • Description: Pajek network: World Soccer, Paris 1998
  • download as a MATLAB mat-file, file size: 2 KB. Use SJget(123) or SJget('Pajek/football') 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.


    scc of Pajek/football

    Pajek/football graph

    Matrix properties (click for a legend)  
    number of rows35
    number of columns35
    structural full rank?no
    structural rank19
    numerical rank 19
    dimension of the numerical null space16
    numerical rank / min(size(A))0.54286
    Euclidean norm of A 23.039
    calculated singular value # 190.13839
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 209.5575e-016
    gap in the singular values at the numerical rank:
    singular value # 19 / singular value # 20
    calculated condition numberInf
    # of blocks from dmperm5
    # strongly connected comp.35
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorL. Krempel
    editorV. Batagelj
    kinddirected weighted graph
    2D/3D problem?no

    Additional fieldssize and type
    nodenamefull 35-by-3
    coordfull 35-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 0.5, and have been removed.  This graph has 2D coordinates.                

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))200 208
    Cholesky flop count1.4e+003 1.5e+003
    nnz(L+U), no partial pivoting365 381
    nnz(V) for QR, upper bound nnz(L) for LU112 125
    nnz(R) for QR, upper bound nnz(U) for LU146 143

    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.