%-------------------------------------------------------------------------------
% SuiteSparse Matrix Collection, Tim Davis
% https://sparse.tamu.edu/SNAP/com-Youtube
% name: SNAP/com-Youtube
% [SNAP network: Youtube social network and ground-truth communities]
% id: 2783
% date: 2012
% author: J. Yang, J. Leskovec
% ed: J. Leskovec
% fields: name title A id date author ed kind notes aux
% aux: nodeid Communities_all Communities_top5000
% kind: undirected graph with communities
%-------------------------------------------------------------------------------
% notes:
% SNAP (Stanford Network Analysis Platform) Large Network Dataset Collection,
% Jure Leskovec and Anrej Krevl, http://snap.stanford.edu/data, June 2014.   
% email: jure at cs.stanford.edu                                             
%                                                                            
% Youtube social network and ground-truth communities                        
%                                                                            
% https://snap.stanford.edu/data/com-Youtube.html                            
%                                                                            
% Dataset information                                                        
%                                                                            
% Youtube (http://www.youtube.com/) is a video-sharing web site that includes
% a social network. In the Youtube social network, users form friendship each
% other and users can create groups which other users can join. We consider  
% such user-defined groups as ground-truth communities. This data is provided
% by Alan Mislove et al.                                                     
% (http://socialnetworks.mpi-sws.org/data-imc2007.html)                      
%                                                                            
% We regard each connected component in a group as a separate ground-truth   
% community. We remove the ground-truth communities which have less than 3   
% nodes.  We also provide the top 5,000 communities with highest quality     
% which are described in our paper (http://arxiv.org/abs/1205.6233). As for  
% the network, we provide the largest connected component.                   
%                                                                            
% Network statistics                                                         
% Nodes   1,134,890                                                          
% Edges   2,987,624                                                          
% Nodes in largest WCC    1134890 (1.000)                                    
% Edges in largest WCC    2987624 (1.000)                                    
% Nodes in largest SCC    1134890 (1.000)                                    
% Edges in largest SCC    2987624 (1.000)                                    
% Average clustering coefficient  0.0808                                     
% Number of triangles 3056386                                                
% Fraction of closed triangles    0.002081                                   
% Diameter (longest shortest path)    20                                     
% 90-percentile effective diameter    6.5                                    
% Community statistics                                                       
% Number of communities   8,385                                              
% Average community size  13.50                                              
% Average membership size 0.10                                               
%                                                                            
% Source (citation)                                                          
% J. Yang and J. Leskovec. Defining and Evaluating Network Communities based 
% on Ground-truth. ICDM, 2012.  http://arxiv.org/abs/1205.6233               
%                                                                            
% Files                                                                      
% File    Description                                                        
% com-youtube.ungraph.txt.gz  Undirected Youtube network                     
% com-youtube.all.cmty.txt.gz Youtube communities                            
% com-youtube.top5000.cmty.txt.gz Youtube communities (Top 5,000)            
%                                                                            
% ---------------------------------------------------------------------------
% Notes on inclusion into the SuiteSparse Matrix Collection, July 2018:      
% ---------------------------------------------------------------------------
%                                                                            
% The graph in the SNAP data set is 1-based, with nodes numbered 1 to        
% 1,157,827.                                                                 
%                                                                            
% In the SuiteSparse Matrix Collection, Problem.A is the undirected Youtube  
% network, a matrix of size n-by-n with n=1,134,890, which is the number of  
% unique user id's appearing in any edge.                                    
%                                                                            
% Problem.aux.nodeid is a list of the node id's that appear in the SNAP data 
% set.  A(i,j)=1 if person nodeid(i) is friends with person nodeid(j).  The  
% node id's are the same as the SNAP data set (1-based).                     
%                                                                            
% C = Problem.aux.Communities_all is a sparse matrix of size n by 16,386     
% which represents the communities in the com-youtube.all.cmty.txt file.     
% The kth line in that file defines the kth community, and is the column     
% C(:,k), where C(i,k)=1 if person nodeid(i) is in the kth community.  Row   
% C(i,:) and row/column i of the A matrix thus refer to the same person,     
% nodeid(i).                                                                 
%                                                                            
% Ctop = Problem.aux.Communities_top5000 is n-by-5000, with the same         
% structure as the C array above, with the content of the                    
% com-youtube.top5000.cmty.txt.gz file.                                      
%-------------------------------------------------------------------------------
