• 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/Erdos992
  • Description: Pajek network: Erdos collaboration network
  • download as a MATLAB mat-file, file size: 146 KB. Use SJget(531) or SJget('Pajek/Erdos992') in MATLAB.
  • download in Matrix Market format, file size: 69 KB.
  • download in Rutherford/Boeing format, file size: 64 KB.


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


    scc of Pajek/Erdos992

    Matrix properties (click for a legend)  
    number of rows6,100
    number of columns6,100
    structural full rank?no
    structural rank922
    numerical rank 922
    dimension of the numerical null space5,178
    numerical rank / min(size(A))0.15115
    Euclidean norm of A 15.131
    calculated singular value # 9220.47037
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 9234.8232e-014
    gap in the singular values at the numerical rank:
    singular value # 922 / singular value # 923
    calculated condition number2.0175e+139
    # of blocks from dmperm50
    # strongly connected comp.1,023
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?no

    authorJ. Grossman, P. Iain, R. Castro
    editorV. Batagelj
    kindundirected graph
    2D/3D problem?no

    Additional fieldssize and type
    clusterfull 6100-by-1
    nodenamefull 6100-by-40


    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'))30,176 41,497
    Cholesky flop count1.7e+006 3.5e+006
    nnz(L+U), no partial pivoting54,252 76,894
    nnz(V) for QR, upper bound nnz(L) for LU1,620,511 1,544,772
    nnz(R) for QR, upper bound nnz(U) for LU381,699 439,257

    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.