(735 graphs) daily instances(graphs) from 11/8/97-1/2/00
Name as-735
Group SNAP
Matrix ID 2320
Num Rows 7,716
Num Cols 7,716
Nonzeros 26,467
Pattern Entries 26,467
Kind Undirected Graph Sequence
Symmetric Yes
Date 2000
Author D. Meyer
Editor J. Leskovec
Structural Rank
Structural Rank Full
Num Dmperm Blocks
Strongly Connect Components 1,243
Num Explicit Zeros 0
Pattern Symmetry 100%
Numeric Symmetry 100%
Cholesky Candidate no
Positive Definite no
Type binary
SVD Statistics
Matrix Norm 4.689263e+01
Minimum Singular Value 0
Condition Number Inf
Rank 2,875
Null Space Dimension 4,841
Full Numerical Rank? no
Download Singular Values MATLAB
Download MATLAB Rutherford Boeing Matrix Market
Networks from SNAP (Stanford Network Analysis Platform) Network Data Sets,    
Jure Leskovec                        
email jure at                                                 
Autonomous systems AS-735                                                     
Dataset information                                                           
The graph of routers comprising the Internet can be organized into sub-graphs 
called Autonomous Systems (AS). Each AS exchanges traffic flows with some     
neighbors (peers). We can construct a communication network of who-talks-to-  
whom from the BGP (Border Gateway Protocol) logs.                             
The data was collected from University of Oregon Route Views Project          
( - Online data and reports. The dataset contains  
735 daily instances which span an interval of 785 days from November 8 1997 to
January 2 2000. In contrast to citation networks, where nodes and edges only  
get added (not deleted) over time, the AS dataset also exhibits both the      
addition and deletion of the nodes and edges over time.                       
Dataset statistics are calculated for the graph with the highest number of    
nodes and edges (dataset from January 02 2000):                               
Dataset statistics                                                            
Nodes   6474                                                                  
Edges   13233                                                                 
Nodes in largest WCC    6474 (1.000)                                          
Edges in largest WCC    13233 (1.000)                                         
Nodes in largest SCC    6474 (1.000)                                          
Edges in largest SCC    13233 (1.000)                                         
Average clustering coefficient  0.3913                                        
Number of triangles     6584                                                  
Fraction of closed triangles    0.009591                                      
Diameter (longest shortest path)    9                                         
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.                
File    Description                                                           
as20000102.txt.gz   Autonomous Systems graph from January 02 2000             
as.tar.gz   735 Autonomous Systems graphs from November 8 1997 to             
             January 02 2000                                                  
NOTE:  In the UF collection, the primary matrix (Problem.A) is the            
as20000102 matrix from January 02 2000 (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.