• SJSU Singular Matrix Database
• Matrix group: Pajek

• Matrix: Pajek/GD06_theory
• Description: Pajek network: Graph Drawing contest 2006
• download as a MATLAB mat-file, file size: 2 KB. Use SJget(19) or SJget('Pajek/GD06_theory') 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 101 number of columns 101 structural full rank? no structural rank 20 numerical rank 20 dimension of the numerical null space 81 numerical rank / min(size(A)) 0.19802 Euclidean norm of A 6.7823 calculated singular value # 20 4 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 8.9706e-014 calculated singular value # 21 3.3193e-015 gap in the singular values at the numerical rank: singular value # 20 / singular value # 21 1.2051e+015 calculated condition number 1.5914e+050 condest Inf nonzeros 380 # of blocks from dmperm 2 # strongly connected comp. 1 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type binary structure symmetric Cholesky candidate? yes positive definite? no

 author Graph Drawing Contest editor V. Batagelj date 2006 kind undirected graph 2D/3D problem? no SJid 19 UFid 1,484

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,
------------------------------------------------------------------------------
GD 2006 contest graph A: Theory
http://gd2006.org/contest/details.php#theory
graph in Pajek format
transformed by Vladimir Batagelj, July 10, 2006
```

 Ordering statistics: AMD METIS nnz(chol(P*(A+A'+s*I)*P')) 336 336 Cholesky flop count 1.3e+003 1.3e+003 nnz(L+U), no partial pivoting 571 571 nnz(V) for QR, upper bound nnz(L) for LU 721 721 nnz(R) for QR, upper bound nnz(U) for LU 3,401 3,401

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.