• 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/CSphd
  • Description: Pajek network: PhD's in computer science
  • download as a MATLAB mat-file, file size: 37 KB. Use SJget(1) or SJget('Pajek/CSphd') in MATLAB.
  • download in Matrix Market format, file size: 24 KB.
  • download in Rutherford/Boeing format, file size: 24 KB.


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


    scc of Pajek/CSphd

    Matrix properties (click for a legend)  
    number of rows1,882
    number of columns1,882
    structural full rank?no
    structural rank706
    numerical rank 705
    dimension of the numerical null space1,177
    numerical rank / min(size(A))0.3746
    Euclidean norm of A 6.7099
    calculated singular value # 7050.61803
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 7068.3884e-015
    gap in the singular values at the numerical rank:
    singular value # 705 / singular value # 706
    calculated condition numberInf
    # of blocks from dmperm408
    # strongly connected comp.1,882
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

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

    Additional fieldssize and type
    phdyearfull 1882-by-1
    nodenamefull 1882-by-32


    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'))3,702 3,893
    Cholesky flop count7.6e+003 8.9e+003
    nnz(L+U), no partial pivoting5,522 5,904
    nnz(V) for QR, upper bound nnz(L) for LU1,907 1,908
    nnz(R) for QR, upper bound nnz(U) for LU6,824 6,824

    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.