• 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/Erdos971
  • Description: Pajek network: Erdos collaboration network
  • download as a MATLAB mat-file, file size: 15 KB. Use SJget(3) or SJget('Pajek/Erdos971') 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/Erdos971

    Matrix properties (click for a legend)  
    number of rows472
    number of columns472
    structural full rank?no
    structural rank414
    numerical rank 413
    dimension of the numerical null space59
    numerical rank / min(size(A))0.875
    Euclidean norm of A 16.71
    calculated singular value # 4130.0042013
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 4142.2488e-015
    gap in the singular values at the numerical rank:
    singular value # 413 / singular value # 414
    calculated condition numberInf
    # of blocks from dmperm230
    # strongly connected comp.42
    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 472-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'))4,400 5,037
    Cholesky flop count1.2e+005 1.5e+005
    nnz(L+U), no partial pivoting8,328 9,602
    nnz(V) for QR, upper bound nnz(L) for LU10,914 10,080
    nnz(R) for QR, upper bound nnz(U) for LU22,181 23,433

    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.