• 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/California
  • Description: Pajek network: Kleinberg's web search of "California"
  • download as a MATLAB mat-file, file size: 377 KB. Use SJget(297) or SJget('Pajek/California') in MATLAB.
  • download in Matrix Market format, file size: 177 KB.
  • download in Rutherford/Boeing format, file size: 171 KB.


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


    scc of Pajek/California

    Matrix properties (click for a legend)  
    number of rows9,664
    number of columns9,664
    structural full rank?no
    structural rank1,686
    numerical rank 1,647
    dimension of the numerical null space8,017
    numerical rank / min(size(A))0.17043
    Euclidean norm of A 21.551
    calculated singular value # 16470.1324
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 16482.2728e-014
    gap in the singular values at the numerical rank:
    singular value # 1647 / singular value # 1648
    calculated condition numberInf
    # of blocks from dmperm541
    # strongly connected comp.9,450
    explicit zero entries0
    nonzero pattern symmetry 2%
    numeric value symmetry 2%
    Cholesky candidate?no
    positive definite?no

    authorJ. Kleinberg
    editorV. Batagelj
    kinddirected graph
    2D/3D problem?no

    Additional fieldssize and type
    nodenamefull 9664-by-128


    Pajek network converted to sparse adjacency matrix for inclusion in UF sparse 
    matrix collection, Tim Davis.  For Pajek datasets, See V. Batagelj & A. Mrvar,
     California - Pages matching the query "California".                          
     This graph was constructed by expanding a 200-page response set to           
     a search engine query 'California', as in the hub/authority algorithm.       
     from Jon Kleinberg:                                                          
     adapted for Pajek, V. Batagelj, March 19, 2006                               
       0 -> 9664                                                                  

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))112,069 138,984
    Cholesky flop count2.0e+007 2.9e+007
    nnz(L+U), no partial pivoting214,474 268,304
    nnz(V) for QR, upper bound nnz(L) for LU1,019,740 1,063,679
    nnz(R) for QR, upper bound nnz(U) for LU120,302 141,417

    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.