%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/SNAP/as-caida
% name: SNAP/as-caida
% [(122 graphs) CAIDA AS Relationships Datasets, from 1/04-11/07]
% id: 2322
% date: 2007
% author: J. Leskovec, J. Kleinberg and C. Faloutsos
% ed: J. Leskovec
% fields: name title A id date author ed kind notes aux
% aux: G Gname nodename
% kind: directed weighted graph sequence
%-------------------------------------------------------------------------------
% 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.                           
%-------------------------------------------------------------------------------
