• 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/Erdos991
  • Description: Pajek network: Erdos collaboration network
  • download as a MATLAB mat-file, file size: 15 KB. Use SJget(5) or SJget('Pajek/Erdos991') in MATLAB.
  • download in Matrix Market format, file size: 9 KB.
  • download in Rutherford/Boeing format, file size: 8 KB.


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


    scc of Pajek/Erdos991

    Matrix properties (click for a legend)  
    number of rows492
    number of columns492
    structural full rank?no
    structural rank436
    numerical rank 435
    dimension of the numerical null space57
    numerical rank / min(size(A))0.88415
    Euclidean norm of A 17.125
    calculated singular value # 4350.0022874
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 4362.1187e-015
    gap in the singular values at the numerical rank:
    singular value # 435 / singular value # 436
    calculated condition numberInf
    # of blocks from dmperm184
    # strongly connected comp.43
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?unknown

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

    Additional fieldssize and type
    nodenamefull 492-by-33


    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'))5,010 5,488
    Cholesky flop count1.5e+005 1.7e+005
    nnz(L+U), no partial pivoting9,528 10,484
    nnz(V) for QR, upper bound nnz(L) for LU13,154 10,649
    nnz(R) for QR, upper bound nnz(U) for LU25,148 25,916

    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.