%-------------------------------------------------------------------------------
% SuiteSparse Matrix Collection, Tim Davis
% https://sparse.tamu.edu/SNAP/higgs-twitter
% name: SNAP/higgs-twitter
% [SNAP network: Higgs Twitter dataset]
% id: 2786
% date: 2015
% author: M. De Domenico, A. Lima, P. Mougel and M. Musolesi
% ed: J. Leskovec
% fields: name title A id date author ed kind notes aux
% aux: retweet reply mention temporal_edges
% kind: directed temporal multigraph
%-------------------------------------------------------------------------------
% 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                                             
%                                                                            
% Higgs Twitter Dataset                                                      
%                                                                            
% https://snap.stanford.edu/data/higgs-twitter.html                          
%                                                                            
% Dataset information                                                        
%                                                                            
% The Higgs dataset has been built after monitoring the spreading processes  
% on Twitter before, during and after the announcement of the discovery of a 
% new particle with the features of the elusive Higgs boson on 4th July 2012.
% The messages posted in Twitter about this discovery between 1st and 7th    
% July 2012 are considered.                                                  
%                                                                            
% The four directional networks made available here have been extracted from 
% user activities in Twitter as:                                             
%                                                                            
%     1. re-tweeting (retweet network)                                       
%     2. replying (reply network) to existing tweets                         
%     3. mentioning (mention network) other users                            
%     4. friends/followers social relationships among user involved          
%        in the above activities                                             
%     5. information about activity on Twitter during the discovery of       
%        Higgs boson                                                         
%                                                                            
% It is worth remarking that the user IDs have been anonimized, and the same 
% user ID is used for all networks. This choice allows to use the Higgs      
% dataset in studies about large-scale interdependent/interconnected         
% multiplex/multilayer networks, where one layer accounts for the social     
% structure and three layers encode different types of user dynamics.        
%                                                                            
% For more information about data collection, please refer to our paper.     
%                                                                            
% Dataset statistics are calculated for the graph with the highest number of 
% nodes and edges:                                                           
%                                                                            
% Social Network statistics                                                  
% Nodes   456,626                                                            
% Edges   14,855,842                                                         
% Nodes in largest WCC    456290 (0.999)                                     
% Edges in largest WCC    14855466 (1.000)                                   
% Nodes in largest SCC    360210 (0.789)                                     
% Edges in largest SCC    14102605 (0.949)                                   
% Average clustering coefficient  0.1887                                     
% Number of triangles 83023401                                               
% Fraction of closed triangles    0.002901                                   
% Diameter (longest shortest path)    9                                      
% 90-percentile effective diameter    3.7                                    
%                                                                            
% Retweet Network statistics                                                 
% Nodes   256,491                                                            
% Edges   328,132                                                            
% Nodes in largest WCC    223833 (0.873)                                     
% Edges in largest WCC    308596 (0.940)                                     
% Nodes in largest SCC    984 (0.004)                                        
% Edges in largest SCC    3850 (0.012)                                       
% Average clustering coefficient  0.0156                                     
% Number of triangles 21172                                                  
% Fraction of closed triangles    0.0001085                                  
% Diameter (longest shortest path)    19                                     
% 90-percentile effective diameter    6.8                                    
%                                                                            
% Reply Network statistics                                                   
% Nodes   38,918                                                             
% Edges   32,523                                                             
% Nodes in largest WCC    12839 (0.330)                                      
% Edges in largest WCC    14944 (0.459)                                      
% Nodes in largest SCC    322 (0.008)                                        
% Edges in largest SCC    708 (0.022)                                        
% Average clustering coefficient  0.0058                                     
% Number of triangles 244                                                    
% Fraction of closed triangles    0.0001561                                  
% Diameter (longest shortest path)    29                                     
% 90-percentile effective diameter    10                                     
%                                                                            
% Mention Network statistics                                                 
% Nodes   116,408                                                            
% Edges   150,818                                                            
% Nodes in largest WCC    91606 (0.787)                                      
% Edges in largest WCC    132068 (0.876)                                     
% Nodes in largest SCC    1801 (0.015)                                       
% Edges in largest SCC    7069 (0.047)                                       
% Average clustering coefficient  0.0825                                     
% Number of triangles 23068                                                  
% Fraction of closed triangles    0.0002417                                  
% Diameter (longest shortest path)    18                                     
% 90-percentile effective diameter    6.5                                    
%                                                                            
% Data format - higgs-activity_time.txt                                      
%                                                                            
%     userA userB timestamp interaction                                      
%                                                                            
%     Interaction can be RT (retweet), MT (mention) or RE (reply). Each link 
%     is directed. The user IDs in this dataset corresponds to the ones      
%     adopted to anonymize the social structure, thus the datasets (1) - (5) 
%     can be used together for complex analysis involving structure and      
%     dynamics.                                                              
%                                                                            
%     Note 1: the direction of links depends on the application, in general. 
%     For instance, if one is interested in building a network of how        
%     information flows, then the direction of RT should be reversed when    
%     used in the analysis. Nevertheless, the choice is left to the          
%     researcher and his/her own interpretation of the data, whereas we just 
%     provide the observed actions, i.e., who                                
%     retweets/mentions/replies/follows whom.                                
%                                                                            
%     Note 2: users mentioned in retweeted tweets are considered as mentions.
%     For instance, if @A retweets the tweet “hello @C @D" sent by @B, then  
%     the following links are created: @A @B timeX RT, @A @C timeX MT, @A @D 
%     timeX MT, because @C and @D can be notified that they have been        
%     mentioned in a retweet. Similarly in the case of a reply. If for some  
%     reason the researcher does not agree with this choice, he/she can      
%     easily identify this type of links and remove the mentions, for        
%     instance.                                                              
%                                                                            
% Source (citation)                                                          
% M. De Domenico, A. Lima, P. Mougel and M. Musolesi. The Anatomy of a       
% Scientific Rumor. (Nature Open Access) Scientific Reports 3, 2980 (2013).  
% http://www.nature.com/srep/2013/131018/srep02980/full/srep02980.html       
%                                                                            
% Files                                                                      
% File    Description                                                        
% social_network.edgelist.gz  Friends/follower graph (directed)              
% retweet_network.edgelist.gz                                                
%     Graph of who retweets whom (directed and weighted)                     
% reply_network.edgelist.gz                                                  
%     Graph of who replies to who (directed and weighted)                    
% mention_network.edgelist.gz                                                
%     Graph of who mentions whom (directed and weighted)                     
% higgs-activity_time.txt.gz                                                 
%     The dataset provides information about activity on                     
%     Twitter during the discovery of Higgs boson                            
%                                                                            
% ---------------------------------------------------------------------------
% Notes on inclusion into the SuiteSparse Matrix Collection, July 2018:      
% ---------------------------------------------------------------------------
%                                                                            
% The SNAP data set is 1-based, with all nodes in all graphs numbered 1      
% to n=456,626.                                                              
%                                                                            
% In the SuiteSparse Matrix Collection, each matrix is the same size, n-by-n 
% where n=456,626, so that row/column i in each matrix refers to the same    
% person i across all matrices.  This means that some rows and columns of    
% the Retweet, Mention, and Reply matrices are empty, but these are left in  
% so all four matrices can be compared with each other.                      
%                                                                            
% Problem.A is the primary social network, and is a directed graph           
% with no edge weights (an unsymmetric binary matrix).  A(i,j)=1 if          
% person i follows person j.  It is not a multigraph.                        
%                                                                            
% Retweet = Problem.aux.retweet is the Retweet network, where Retweet(i,j)   
% is the number of times that person i retweets a tweet of person j.         
%                                                                            
% Mention = Problem.aux.mention is the Mention network, where Mention(i,j)   
% is the number of times that person i mentions person j.                    
%                                                                            
% Reply = Problem.aux.reply is the Reply network, where Reply(i,j)           
% is the number of times that person i replies to person j.                  
%                                                                            
% The Retweet, Mention, and Reply matrices represent multigraphs since each  
% (i,j,t) with the same i and j but different timestamp t is considered a    
% separate edge.  The timestamps do not appear in these matrices, however.   
%                                                                            
% The higgs-activity_time.txt is a set of labeled temporal edges.  Each edge 
% in the SNAP data set has the form (i,j,time,interaction) where interaction 
% is string (RT, MT, or RE).  In the SuiteSparse Matrix collection, these    
% edges are stored as a dense matrix, Problem.aux.temporal_edges, where the  
% kth row of the matrix holds the kth line of the higgs-activity_time.txt    
% file as the temporal edge [i j interaction time].  The interaction is      
% converted to an integer, where 1=RT (retweet), 2=MT (mention), and 3=RE    
% (reply).                                                                   
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