Matrix: SNAP/as-735

Description: (735 graphs) daily instances(graphs) from 11/8/97-1/2/00

SNAP/as-735 graph
(undirected graph drawing)


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  • download as a MATLAB mat-file, file size: 26 MB. Use UFget(2320) or UFget('SNAP/as-735') in MATLAB.
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  • download in Rutherford/Boeing format, file size: 17 MB.

    Matrix properties
    number of rows7,716
    number of columns7,716
    # strongly connected comp.1,243
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

    authorD. Meyer
    editorJ. Leskovec
    kindundirected graph sequence
    2D/3D problem?no

    Additional fieldssize and type
    Gcell 733-by-1
    Gnamefull 733-by-10
    nodenamefull 7716-by-1


    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.                          

    SVD-based statistics:
    null space dimension4,841
    full numerical rank?no
    singular value gap5.08366e+11

    singular values (MAT file):click here
    SVD method used:s = svd (full (A)) ;

    SNAP/as-735 svd

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 12-Mar-2014.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.