{
    matrix_id: '2322',
    name: 'as-caida',
    group: 'SNAP',
    description: '(122 graphs) CAIDA AS Relationships Datasets, from 1/04-11/07',
    author: 'J. Leskovec, J. Kleinberg and C. Faloutsos',
    editor: 'J. Leskovec',
    date: '2007',
    kind: 'directed weighted graph sequence',
    problem_2D_or_3D: '0',
    num_rows: '31379',
    num_cols: '31379',
    nonzeros: '106762',
    num_explicit_zeros: '0',
    num_strongly_connected_components: '4905',
    pattern_symmetry: '1.000',
    numeric_symmetry: '0.079',
    rb_type: 'integer',
    structure: 'unsymmetric',
    cholesky_candidate: 'no',
    positive_definite: 'no',
    notes: 'Networks from SNAP (Stanford Network Analysis Platform) Network Data Sets,     
Jure Leskovec http://snap.stanford.edu/data/index.html                         
email jure at cs.stanford.edu                                                  
                                                                               
CAIDA AS Relationships Datasets                                                
Dataset information                                                            
                                                                               
The dataset contains 122 CAIDA AS graphs, from January 2004 to November 2007 - 
http://www.caida.org/data/active/as-relationships/ .  Each file contains a full
AS graph derived from a set of RouteViews BGP table snapshots.                 
                                                                               
Dataset statistics are calculated for the graph with the highest number of     
nodes - dataset from November 5 2007.  Dataset statistics for graph with       
highest number of nodes - 11 5 2007                                            
                                                                               
Nodes   26475                                                                  
Edges   106762                                                                 
Nodes in largest WCC    26475 (1.000)                                          
Edges in largest WCC    106762 (1.000)                                         
Nodes in largest SCC    26475 (1.000)                                          
Edges in largest SCC    106762 (1.000)                                         
Average clustering coefficient  0.2082                                         
Number of triangles     36365                                                  
Fraction of closed triangles    0.007319                                       
Diameter (longest shortest path)    17                                         
90-percentile effective diameter    4.6                                        
                                                                               
Source (citation)                                                              
                                                                               
J. Leskovec, J. Kleinberg and C. Faloutsos. Graphs over Time: Densification    
Laws, Shrinking Diameters and Possible Explanations. ACM SIGKDD International  
Conference on Knowledge Discovery and Data Mining (KDD), 2005.                 
                                                                               
Files                                                                          
File    Description                                                            
as-caida20071105.txt.gz     CAIDA AS graph from November 5 2007                
as-caida.tar.gz     122 CAIDA AS graphs from January 2004 to November 2007     
                                                                               
                                                                               
NOTE for UF Sparse Matrix Collection: these graphs are weighted.  In the       
original SNAP data set, the edge weights are in the set {-1, 0, 1, 2}.  Note   
that "0" is an edge weight.  This can be handled in the UF collection for the  
primary sparse matrix in a Problem, but not when the matrices are in a sequence
in the Problem.aux MATLAB struct.  The entries with zero edge weight would     
become lost.  To correct for this, the weights are modified by adding 2 to each
weight.  This preserves the structure of the original graphs, so that edges    
with weight zero are not lost.  (A non-edge is not the same as an edge with    
weight zero in this problem).                                                  
                                                                               
    old new weights:                                                           
    -1  1                                                                      
    0   2                                                                      
    1   3                                                                      
    2   4                                                                      
                                                                               
So to obtain the original weights, subtract 2 from each entry.                 
                                                                               
The primary sparse matrix for this problem is the as-caida20071105 matrix, or  
Problem.aux.G{121}, the second-to-the-last graph in the sequence.              
                                                                               
The nodes are uniform across all graphs in the sequence in the UF collection.  
That is, nodes do not come and go.  A node that is "gone" simply has no edges. 
This is to allow comparisons across each node in the graphs.                   
Problem.aux.nodenames gives the node numbers of the original problem.  So      
row/column i in the matrix is always node number Problem.aux.nodenames(i) in   
all the graphs.                                                                
                                                                               
Problem.aux.G{k} is the kth graph in the sequence.                             
Problem.aux.Gname(k,:) is the name of the kth graph.                           
',
    aux_fields: 'G: cell 122-by-1
Gname: full 122-by-16
nodename: full 31379-by-1
',    norm: '1.822487e+02',
    min_singular_value: '0',
    condition_number: 'Inf',
    svd_rank: '7360',
    null_space_dimension: '24019',
    full_numerical_rank: 'no',
    svd_gap: '2563654870.997341',
    image_files: 'as-caida.png,as-caida_svd.png,as-caida_graph.gif,',
}
