• SJSU Singular Matrix Database
• Matrix group: Pajek

• Matrix: Pajek/GD97_b
• Description: Pajek network: Graph Drawing contest 1997
• download as a MATLAB mat-file, file size: 5 KB. Use SJget(27) or SJget('Pajek/GD97_b') 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 47 number of columns 47 structural full rank? no structural rank 44 numerical rank 44 dimension of the numerical null space 3 numerical rank / min(size(A)) 0.93617 Euclidean norm of A 2841.1 calculated singular value # 44 0.00053395 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 2.1373e-011 calculated singular value # 45 1.4045e-014 gap in the singular values at the numerical rank: singular value # 44 / singular value # 45 3.8017e+010 calculated condition number Inf condest Inf nonzeros 264 # of blocks from dmperm 24 # strongly connected comp. 2 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type real structure symmetric Cholesky candidate? yes positive definite? no

 author Graph Drawing Contest editor V. Batagelj date 1997 kind undirected weighted graph 2D/3D problem? no SJid 27 UFid 1,493

 Additional fields size and type nodename full 47-by-30 coord full 47-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,
------------------------------------------------------------------------------
Regarding conversion for UF sparse matrix collection: in the original data
every edge appears exactly twice, with the same edge weight.  It could be a
multigraph, but it looks more like a graph.  The duplicate edges are removed
in this version.  You can always add them back in yourself; just look at 2*A.
------------------------------------------------------------------------------
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')) 211 220 Cholesky flop count 1.0e+003 1.1e+003 nnz(L+U), no partial pivoting 375 393 nnz(V) for QR, upper bound nnz(L) for LU 401 274 nnz(R) for QR, upper bound nnz(U) for LU 719 770

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.