• 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/SmaGri
  • Description: Pajek network: SmaGri citation network
  • download as a MATLAB mat-file, file size: 26 KB. Use SJget(44) or SJget('Pajek/SmaGri') in MATLAB.
  • download in Matrix Market format, file size: 21 KB.
  • download in Rutherford/Boeing format, file size: 17 KB.


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


    scc of Pajek/SmaGri

    Matrix properties (click for a legend)  
    number of rows1,059
    number of columns1,059
    structural full rank?no
    structural rank513
    numerical rank 511
    dimension of the numerical null space548
    numerical rank / min(size(A))0.48253
    Euclidean norm of A 21.63
    calculated singular value # 5110.10403
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 5122.4874e-014
    gap in the singular values at the numerical rank:
    singular value # 511 / singular value # 512
    calculated condition numberInf
    # of blocks from dmperm144
    # strongly connected comp.1,057
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorE. Garfield
    editorV. Batagelj
    kinddirected multigraph
    2D/3D problem?no

    Additional fieldssize and type
    pubyearfull 1059-by-1
    gcsfull 1059-by-1
    nodenamefull 1059-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,
     Citations to Small & Griffith and Descendants, Thu Nov 8 10:40:55 2001       

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))26,721 29,446
    Cholesky flop count2.6e+006 2.8e+006
    nnz(L+U), no partial pivoting52,383 57,833
    nnz(V) for QR, upper bound nnz(L) for LU7,984 4,592
    nnz(R) for QR, upper bound nnz(U) for LU187,117 193,409

    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.