• 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/Roget
  • Description: Pajek network: Roget's Thesaurus, 1879
  • download as a MATLAB mat-file, file size: 25 KB. Use SJget(41) or SJget('Pajek/Roget') in MATLAB.
  • download in Matrix Market format, file size: 19 KB.
  • download in Rutherford/Boeing format, file size: 16 KB.


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


    scc of Pajek/Roget

    Matrix properties (click for a legend)  
    number of rows1,022
    number of columns1,022
    structural full rank?no
    structural rank986
    numerical rank 984
    dimension of the numerical null space38
    numerical rank / min(size(A))0.96282
    Euclidean norm of A 9.0068
    calculated singular value # 9840.0016123
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 9851.6415e-015
    gap in the singular values at the numerical rank:
    singular value # 984 / singular value # 985
    calculated condition numberInf
    # of blocks from dmperm162
    # strongly connected comp.77
    explicit zero entries0
    nonzero pattern symmetry 56%
    numeric value symmetry 56%
    Cholesky candidate?no
    positive definite?no

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

    Additional fieldssize and type
    nodenamefull 1022-by-23


    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'))49,572 51,205
    Cholesky flop count7.7e+006 7.1e+006
    nnz(L+U), no partial pivoting98,122 101,388
    nnz(V) for QR, upper bound nnz(L) for LU85,325 70,215
    nnz(R) for QR, upper bound nnz(U) for LU118,051 126,444

    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.