Matrix: SNAP/as-caida

Description: (122 graphs) CAIDA AS Relationships Datasets, from 1/04-11/07

SNAP/as-caida graph
(undirected graph drawing)


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  • download as a MATLAB mat-file, file size: 28 MB. Use UFget(2322) or UFget('SNAP/as-caida') in MATLAB.
  • download in Matrix Market format, file size: 38 MB.
  • download in Rutherford/Boeing format, file size: 33 MB.

    Matrix properties
    number of rows31,379
    number of columns31,379
    # strongly connected comp.4,905
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetry 8%
    Cholesky candidate?no
    positive definite?no

    authorJ. Leskovec, J. Kleinberg and C. Faloutsos
    editorJ. Leskovec
    kinddirected weighted graph sequence
    2D/3D problem?no

    Additional fieldssize and type
    Gcell 122-by-1
    Gnamefull 122-by-16
    nodenamefull 31379-by-1


    Networks from SNAP (Stanford Network Analysis Platform) Network Data Sets,     
    Jure Leskovec                         
    email jure at                                                  
    CAIDA AS Relationships Datasets                                                
    Dataset information                                                            
    The dataset contains 122 CAIDA AS graphs, from January 2004 to November 2007 - .  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.                 
    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.                           

    SVD-based statistics:
    null space dimension24,019
    full numerical rank?no
    singular value gap2.56365e+09

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

    SNAP/as-caida 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.