• 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/USAir97
  • Description: Pajek network: US Air flights, 1997
  • download as a MATLAB mat-file, file size: 34 KB. Use SJget(49) or SJget('Pajek/USAir97') in MATLAB.
  • download in Matrix Market format, file size: 16 KB.
  • download in Rutherford/Boeing format, file size: 14 KB.

    Pajek/USAir97

    Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

    Pajek/USAir97

    Pajek/USAir97 graph

    Matrix properties (click for a legend)  
    number of rows332
    number of columns332
    structural full rank?no
    structural rank281
    numerical rank 281
    dimension of the numerical null space51
    numerical rank / min(size(A))0.84639
    Euclidean norm of A 4.2268
    calculated singular value # 2814.7967e-007
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.9488e-013
    calculated singular value # 2821.763e-016
    gap in the singular values at the numerical rank:
    singular value # 281 / singular value # 282
    2.7207e+009
    calculated condition number9.0041e+020
    condestInf
    nonzeros4,252
    # of blocks from dmperm88
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typereal
    structuresymmetric
    Cholesky candidate?yes
    positive definite?no

    authorUS Air
    editorV. Batagelj
    date1997
    kindundirected weighted graph
    2D/3D problem?no
    SJid49
    UFid1,529

    Additional fieldssize and type
    nodenamefull 332-by-30
    coordfull 332-by-2

    Notes:

    ------------------------------------------------------------------------------
    Pajek network converted to sparse adjacency matrix for inclusion in UF sparse 
    matrix collection, Tim Davis.  For Pajek datasets, See V. Batagelj & A. Mrvar,
    http://vlado.fmf.uni-lj.si/pub/networks/data/.                                
    ------------------------------------------------------------------------------
    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'))2,908 3,073
    Cholesky flop count5.1e+004 5.8e+004
    nnz(L+U), no partial pivoting5,484 5,814
    nnz(V) for QR, upper bound nnz(L) for LU10,708 4,108
    nnz(R) for QR, upper bound nnz(U) for LU23,454 23,957

    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.