• 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/GlossGT
  • Description: Pajek network: graph and digraph glossary
  • download as a MATLAB mat-file, file size: 4 KB. Use SJget(34) or SJget('Pajek/GlossGT') in MATLAB.
  • download in Matrix Market format, file size: 2 KB.
  • download in Rutherford/Boeing format, file size: 2 KB.

    Pajek/GlossGT

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

    Pajek/GlossGT

    scc of Pajek/GlossGT

    Pajek/GlossGT graph

    Matrix properties (click for a legend)  
    number of rows72
    number of columns72
    structural full rank?no
    structural rank35
    numerical rank 35
    dimension of the numerical null space37
    numerical rank / min(size(A))0.48611
    Euclidean norm of A 5.4062
    calculated singular value # 350.3362
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    6.3949e-014
    calculated singular value # 367.9729e-016
    gap in the singular values at the numerical rank:
    singular value # 35 / singular value # 36
    4.2168e+014
    calculated condition numberInf
    condestInf
    nonzeros122
    # of blocks from dmperm17
    # strongly connected comp.68
    explicit zero entries0
    nonzero pattern symmetry 7%
    numeric value symmetry 7%
    typebinary
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorW. Cherowitzo
    editorV. Batagelj
    date2001
    kinddirected graph
    2D/3D problem?no
    SJid34
    UFid1,501

    Additional fieldssize and type
    nodenamefull 72-by-19
    coordfull 72-by-2

    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/.                                
    ------------------------------------------------------------------------------
     Bill Cherowitzo: Graph and Digraph Glossary                                  
     http://www-math.cudenver.edu/~wcherowi/courses/m4408/glossary.html           
     Pajek's network: Barbara Zemlji"c, 2. nov 2003                               
    The original problem had 3D xyz coordinates, but all values of z were equal   
    to 0, and have been removed.  This graph has 2D coordinates.                  
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))246 255
    Cholesky flop count1.1e+003 1.2e+003
    nnz(L+U), no partial pivoting420 438
    nnz(V) for QR, upper bound nnz(L) for LU199 200
    nnz(R) for QR, upper bound nnz(U) for LU147 147

    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.