• 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/internet
  • Description: Pajek network: connectivity of internet routers
  • download as a MATLAB mat-file, file size: 999 KB. Use SJget(354) or SJget('Pajek/internet') in MATLAB.
  • download in Matrix Market format, file size: 1 MB.
  • download in Rutherford/Boeing format, file size: 1 MB.


    A singular value of A is guaranteed1 to be in the interval pictured by the blue bars around each of the calculated singular values.

    Routine svds_err, version 1.0, used with Matlab (R2008a) to calculate the 6 largest singular values and associated error bounds.
    Routine spnrank, version 1.0, used with Matlab (R2008a) to calculate singular values 66596 to 66601 and associated error bounds.


    scc of Pajek/internet

    Matrix properties (click for a legend)  
    number of rows124,651
    number of columns124,651
    structural full rank?no
    structural rank66,679
    numerical rank 66,598
    dimension of the numerical null space58,053
    numerical rank / min(size(A))0.53428
    Euclidean norm of A 6.3872e+005
    calculated singular value # 665982.8283e-005
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 665998.2084e-012
    gap in the singular values at the numerical rank:
    singular value # 66598 / singular value # 66599
    calculated condition number-2
    # of blocks from dmperm33,954
    # strongly connected comp.116,713
    explicit zero entries0
    nonzero pattern symmetry 1%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

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

    Additional fieldssize and type
    nodenamefull 124651-by-15


    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'))2,282,224 2,274,088
    Cholesky flop count2.0e+009 1.5e+009
    nnz(L+U), no partial pivoting4,439,797 4,423,525
    nnz(V) for QR, upper bound nnz(L) for LU153,163 152,695
    nnz(R) for QR, upper bound nnz(U) for LU937,714 934,085

    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.