• 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/EPA
  • Description: Pajek network: Kleinberg, pages linking to www.epa.gov
  • download as a MATLAB mat-file, file size: 169 KB. Use SJget(2) or SJget('Pajek/EPA') in MATLAB.
  • download in Matrix Market format, file size: 82 KB.
  • download in Rutherford/Boeing format, file size: 80 KB.

    Pajek/EPA

    Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

    Pajek/EPA

    scc of Pajek/EPA

    Matrix properties (click for a legend)  
    number of rows4,772
    number of columns4,772
    structural full rank?no
    structural rank986
    numerical rank 951
    dimension of the numerical null space3,821
    numerical rank / min(size(A))0.19929
    Euclidean norm of A 16.158
    calculated singular value # 9510.076126
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.6954e-011
    calculated singular value # 9526.386e-014
    gap in the singular values at the numerical rank:
    singular value # 951 / singular value # 952
    1.1921e+012
    calculated condition numberInf
    condestInf
    nonzeros8,965
    # of blocks from dmperm314
    # strongly connected comp.4,711
    explicit zero entries0
    nonzero pattern symmetry 1%
    numeric value symmetry 1%
    typebinary
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorJ. Kleinberg
    editorV. Batagelj
    date2006
    kinddirected graph
    2D/3D problem?no
    SJid2
    UFid1,463

    Additional fieldssize and type
    nodenamefull 4772-by-106

    Notes:

    ------------------------------------------------------------------------------
    Pajek network converted to sparse adjacency matrix for inclusion in UF sparse 
    matrix collection, Tim Davis.  For Pajek datasets, See V. Batagelj & A. Mrvar,
    http://vlado.fmf.uni-lj.si/pub/networks/data/.                                
    ------------------------------------------------------------------------------
     Epa - Pages linking to www.epa.gov.                                          
     This graph was constructed by expanding a 200-page response set to           
     a search engine query, as in the hub/authority algorithm.                    
     from Jon Kleinberg:                                                          
       http://www.cs.cornell.edu/courses/cs685/2002fa/                            
     adapted for Pajek, V. Batagelj, March 19, 2006                               
       0 -> 4772                                                                  
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))58,313 71,117
    Cholesky flop count7.5e+006 9.8e+006
    nnz(L+U), no partial pivoting111,854 137,462
    nnz(V) for QR, upper bound nnz(L) for LU56,434 62,675
    nnz(R) for QR, upper bound nnz(U) for LU394,097 452,063

    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.