• 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/Erdos02
  • Description: Pajek network: Erdos collaboration network
  • download as a MATLAB mat-file, file size: 165 KB. Use SJget(532) or SJget('Pajek/Erdos02') in MATLAB.
  • download in Matrix Market format, file size: 78 KB.
  • download in Rutherford/Boeing format, file size: 72 KB.


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


    scc of Pajek/Erdos02

    Matrix properties (click for a legend)  
    number of rows6,927
    number of columns6,927
    structural full rank?no
    structural rank938
    numerical rank 938
    dimension of the numerical null space5,989
    numerical rank / min(size(A))0.13541
    Euclidean norm of A 25.842
    calculated singular value # 9380.50881
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 9395.5569e-014
    gap in the singular values at the numerical rank:
    singular value # 938 / singular value # 939
    calculated condition number2.548e+139
    # of blocks from dmperm42
    # strongly connected comp.1,394
    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
    nodenamefull 6927-by-45


    Pajek network converted to sparse adjacency matrix for inclusion in UF sparse 
    matrix collection, Tim Davis.  For Pajek datasets, See V. Batagelj & A. Mrvar,
     Erdos collaboration network:                                                 
     Erdos included, version 2002                                                 

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))33,211 46,009
    Cholesky flop count1.9e+006 4.2e+006
    nnz(L+U), no partial pivoting59,495 85,091
    nnz(V) for QR, upper bound nnz(L) for LU2,488,463 2,381,502
    nnz(R) for QR, upper bound nnz(U) for LU555,374 594,777

    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.