• 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/USpowerGrid
  • Description: Pajek network: US power grid
  • download as a MATLAB mat-file, file size: 66 KB. Use SJget(50) or SJget('Pajek/USpowerGrid') in MATLAB.
  • download in Matrix Market format, file size: 23 KB.
  • download in Rutherford/Boeing format, file size: 22 KB.


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


    Matrix properties (click for a legend)  
    number of rows4,941
    number of columns4,941
    structural full rank?no
    structural rank4,366
    numerical rank 4,348
    dimension of the numerical null space593
    numerical rank / min(size(A))0.87998
    Euclidean norm of A 7.4831
    calculated singular value # 43480.018748
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 43496.0036e-015
    gap in the singular values at the numerical rank:
    singular value # 4348 / singular value # 4349
    calculated condition number6.0341e+033
    # of blocks from dmperm1,968
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?no

    authorP. Tsaparas
    editorV. Batagelj
    kindundirected graph
    2D/3D problem?no


    Pajek network converted to sparse adjacency matrix for inclusion in UF sparse 
    matrix collection, Tim Davis.  For Pajek datasets, See V. Batagelj & A. Mrvar,
     US power grid - unweighted network                                           
     from Panayiotis Tsaparas:                                                    
     adapted for Pajek, V. Batagelj, March 19, 2006                               
       0 -> 4941                                                                  

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))16,742 18,732
    Cholesky flop count7.9e+004 1.2e+005
    nnz(L+U), no partial pivoting28,543 32,523
    nnz(V) for QR, upper bound nnz(L) for LU75,796 49,728
    nnz(R) for QR, upper bound nnz(U) for LU44,214 51,463

    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.