Matrix: Newman/power

Description: Western States Power Grid, Watts & Strogatz

Newman/power graph
(undirected graph drawing)


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  • Matrix group: Newman
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  • download as a MATLAB mat-file, file size: 32 KB. Use UFget(2404) or UFget('Newman/power') in MATLAB.
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  • download in Rutherford/Boeing format, file size: 23 KB.

    Matrix properties
    number of rows4,941
    number of columns4,941
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

    authorD. Watts, S. Strogatz
    editorM. Newman
    kindundirected graph
    2D/3D problem?no


    Network collection from M. Newman                                                                    
    Western States Power Grid                                                  
    Compiled by Duncan Watts and Steven Strogatz                               
    The graph "power" contains an undirected unweighted representation of the  
    topology of the Western States Power Grid of the United States, compiled by
    Duncan Watts and Steven Strogatz.  The data are from the web site of       
    Prof. Duncan Watts at Columbia University,                              Node IDs are the same as those used 
    by Prof. Watts.                                                            
    These data can be cited as:                                                
      D. J. Watts and S. H. Strogatz, "Collective dynamics of `small-world     
      networks", Nature 393, 440-442 (1998).                                   
    Note by Tim Davis: this graph has the same number of nodes and edges       
    as the Pajek/USpowerGrid graph.  They are related as follows:              
       Prob1 = UFget ('Newman/power')                                          
       Prob2 = UFget ('Pajek/USpowerGrid')                                     
       A = Prob1.A ;                                                           
       B = Prob2.B ;                                                           
       n = size (A,1) ;                                                        
       p = [2:n 1] ;                                                           
       isequal (A (p,p), B)                                                    
    This is because of the way the Pajek data set converted 0-based node IDs   
    to 1-based.  In the Pajek set, node 0 is renamed node n, and this          
    translation was then imported into the Pajek/ Group in the UF collection.  
    The standard convention in MATLAB, and (elsewhere) in the UF Collection,   
    is to map nodes 0:n-1 of a zero-based graph to 1:n.  The latter translation
    preserves the relative numbering of all the nodes; the Pajek translation   
    does not.                                                                  
    Although technically Newman/power is a duplicate matrix, I have added it   
    to the UF Collection to preserve the original relative node ordering.      

    SVD-based statistics:
    null space dimension593
    full numerical rank?no
    singular value gap2.23267e+12

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

    Newman/power 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.