Matrix properties
number of rows	19,190
number of columns	19,190
nonzeros	57,162
structural full rank?	yes
structural rank	19,190
# of blocks from dmperm	1
# strongly connected comp.	1
explicit zero entries	0
nonzero pattern symmetry	symmetric
numeric value symmetry	symmetric
type	binary
structure	symmetric
Cholesky candidate?	no
positive definite?	no

author	R. Diekmann, R. Preis
editor	R. Diekmann, R. Preis
date	1998
kind	2D/3D problem
2D/3D problem?	yes

Additional fields	size and type
coord	full 19190-by-2

Notes:

AG-Monien Graph Collection, Ralf Diekmann and Robert Preis                     
http://www2.cs.uni-paderborn.de/fachbereich/AG/monien/RESEARCH/PART/graphs.html
                                                                               
A collection of test graphs from various sources.  Many of the graphs          
include XY or XYZ coordinates.  This set also includes some graphs from        
the Harwell-Boeing collection, the NASA matrices, and some random matrices     
which are not included here in the AG-Monien/ group of the UF Collection.      
In addition, two graphs already appear in other groups:                        
                                                                               
   AG-Monien/big : same as Nasa/barth5, Pothen/barth5 (not included here)      
   AG-Monien/cage_3_11 : same as Pajek/GD98_c (included here)                  
                                                                               
The AG-Monien/GRID subset is not included.  It contains square grids that      
are already well-represented in the UF Collection.                             
                                                                               
Six of the problem sets are included as sequences, each sequence being         
a single problem instance in the UF Collection:                                
                                                                               
   bfly:  10 butterfly graphs 3..12                                            
   cage:  45 cage graphs 3..12                                                 
   cca:   10 cube-connected cycle graphs, no wrap                              
   ccc:   10 cube-connected cycle graphs, with wrap                            
   debr:  18 De Bruijn graphs                                                  
   se:    13 shuffle-exchange graphs                                           
                                                                               
Problem.aux.G{:} are the graphs in these 6 sequences.  Problem.aux.Gname{:}    
are the original names of each graph, and Problemm.aux.Gcoord{:} are the       
xy or xyz coordinates of each node, if present.                                

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	304,008
Cholesky flop count	1.6e+07
nnz(L+U), no partial pivoting, with AMD	588,826
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	527,064
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	974,704

SVD-based statistics:
norm(A)	2.99917
min(svd(A))	3.10811e-17
cond(A)	9.6495e+16
rank(A)	19,163
sprank(A)-rank(A)	27
null space dimension	27
full numerical rank?	no
singular value gap	6.51616

singular values (MAT file):	click here
SVD method used:	s = svd (full (R)) ; where [~,R,E] = spqr (A) with droptol of zero
status:	ok

For a description of the statistics displayed above, click here.

Maintained by Tim Davis, last updated 12-Mar-2014.
Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.