• 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/Erdos972
  • Description: Pajek network: Erdos collaboration network
  • download as a MATLAB mat-file, file size: 132 KB. Use SJget(529) or SJget('Pajek/Erdos972') in MATLAB.
  • download in Matrix Market format, file size: 63 KB.
  • download in Rutherford/Boeing format, file size: 58 KB.


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


    scc of Pajek/Erdos972

    Matrix properties (click for a legend)  
    number of rows5,488
    number of columns5,488
    structural full rank?no
    structural rank882
    numerical rank 882
    dimension of the numerical null space4,606
    numerical rank / min(size(A))0.16071
    Euclidean norm of A 14.448
    calculated singular value # 8820.62708
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 8834.311e-014
    gap in the singular values at the numerical rank:
    singular value # 882 / singular value # 883
    calculated condition number1.0095e+127
    # of blocks from dmperm50
    # strongly connected comp.754
    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 5488-by-1
    nodenamefull 5488-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'))27,041 39,173
    Cholesky flop count1.4e+006 3.6e+006
    nnz(L+U), no partial pivoting48,594 72,858
    nnz(V) for QR, upper bound nnz(L) for LU1,396,200 1,413,816
    nnz(R) for QR, upper bound nnz(U) for LU363,051 403,719

    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.