• SJSU Singular Matrix Database
• Matrix group: Pajek

• Matrix: Pajek/GD01_c
• Description: Pajek network: Graph Drawing contest 2001
• download as a MATLAB mat-file, file size: 2 KB. Use SJget(15) or SJget('Pajek/GD01_c') in MATLAB.

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

 Matrix properties (click for a legend) number of rows 33 number of columns 33 structural full rank? no structural rank 27 numerical rank 25 dimension of the numerical null space 8 numerical rank / min(size(A)) 0.75758 Euclidean norm of A 8.1173 calculated singular value # 25 0.28443 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 5.862e-014 calculated singular value # 26 3.2264e-016 gap in the singular values at the numerical rank: singular value # 25 / singular value # 26 8.8157e+014 calculated condition number Inf condest Inf nonzeros 135 # of blocks from dmperm 9 # strongly connected comp. 33 explicit zero entries 0 nonzero pattern symmetry 0% numeric value symmetry 0% type integer structure unsymmetric Cholesky candidate? no positive definite? no

 author Graph Drawing Contest editor V. Batagelj date 2001 kind directed multigraph 2D/3D problem? no SJid 15 UFid 1,480

 Additional fields size and type partition full 33-by-1 nodename full 33-by-4 coord full 33-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,
------------------------------------------------------------------------------
The original problem had 3D xyz coordinates, but all values of z were equal
to 0.5, and have been removed.  This graph has 2D coordinates.

 Ordering statistics: AMD METIS nnz(chol(P*(A+A'+s*I)*P')) 200 211 Cholesky flop count 1.5e+003 1.7e+003 nnz(L+U), no partial pivoting 367 389 nnz(V) for QR, upper bound nnz(L) for LU 92 84 nnz(R) for QR, upper bound nnz(U) for LU 214 238

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.