• 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/dictionary28
  • Description: Pajek network: dictionary
  • download as a MATLAB mat-file, file size: 534 KB. Use SJget(466) or SJget('Pajek/dictionary28') in MATLAB.
  • download in Matrix Market format, file size: 476 KB.
  • download in Rutherford/Boeing format, file size: 420 KB.


    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 37772 to 37777 and associated error bounds.


    scc of Pajek/dictionary28

    Matrix properties (click for a legend)  
    number of rows52,652
    number of columns52,652
    structural full rank?no
    structural rank38,108
    numerical rank 37,774
    dimension of the numerical null space14,878
    numerical rank / min(size(A))0.71743
    Euclidean norm of A 25.062
    calculated singular value # 377740.00016504
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 377757.3213e-015
    gap in the singular values at the numerical rank:
    singular value # 37774 / singular value # 37775
    calculated condition number-2
    # of blocks from dmperm15,276
    # strongly connected comp.17,903
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?no

    editorV. Batagelj
    kindundirected graph
    2D/3D problem?no

    Additional fieldssize and type
    nodenamefull 52652-by-8


    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'))6,352,200 4,119,600
    Cholesky flop count1.2e+010 4.0e+009
    nnz(L+U), no partial pivoting12,651,748 8,186,548
    nnz(V) for QR, upper bound nnz(L) for LU19,591,555 10,117,692
    nnz(R) for QR, upper bound nnz(U) for LU27,817,185 18,294,354

    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.