Matrix: DIMACS10/ri2010

Description: DIMACS10 set: redistrict/ri2010 and ri2010a

DIMACS10/ri2010 graph
(undirected graph drawing)


DIMACS10/ri2010
scc of DIMACS10/ri2010 DIMACS10/ri2010 graph

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  • download as a MATLAB mat-file, file size: 1 MB. Use UFget(2620) or UFget('DIMACS10/ri2010') in MATLAB.
  • download in Matrix Market format, file size: 698 KB.
  • download in Rutherford/Boeing format, file size: 653 KB.

    Matrix properties
    number of rows25,181
    number of columns25,181
    nonzeros125,750
    # strongly connected comp.2
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typeinteger
    structuresymmetric
    Cholesky candidate?no
    positive definite?no

    authorW. Zhao
    editorH. Meyerhenke
    date2010
    kindundirected weighted graph
    2D/3D problem?no

    Additional fieldssize and type
    populationfull 25181-by-1
    areafull 25181-by-1
    coordfull 25181-by-2

    Notes:

    DIMACS10 redistrict set                                               
                                                                          
    Redistricting and Graph Partitioning                                  
    ====================================                                  
                                                                          
    The xx2010a graphs are generated from U.S. Census 2010 and Tiger/Line 
    2010 shapefiles. They are freely available from census.gov web site.  
    The xx prefix in the filenames are the U.S. Postal Service acronyms of
    the state names, e.g.  ny is New York.                                
                                                                          
    * the vertices are the Census Blocks;                                 
    * two vertices have an edge if and only if the corresponding Census   
        Blocks share a line segment on their border, i.e. rook-style      
        neighboring.                                                      
    * each vertex has two weights:                                        
       (1) Census2010 POP100 or the number of people living in that       
           Census Block, and.                                             
       (2) Land Area of the Census Block in square meters                 
    * the edge weights are the pseudo-length of the shared borderlines.   
        The pseudo-length is calculated using sqrt(x^2 + y^2), x and y    
        being the differences in longitudes and latitudes of each line    
        segment on the shared borderlines.  Then the result is multiplied 
        by 10^7 to make the edge weights integers.                        
    * each Census Block gets identified by a point, and the XY coordinates
        are the longitudes and latitudes of each point.  The points are   
        selected by Census to be internal to the Census Blocks, but the   
        tech doc says that they are not always internal (but always very  
        close).                                                           
                                                                          
    Author: Will Zhao                                                     
    Added to the DIMACS10 collection by Henning Meyerhenke, 2011          
                                                                          
    The DIMACS10 collection also includes versions of these graphs with   
    unweighted edges.  The two sets have been merged in this collection.  
    If you want the unweighted version, just drop the edge weights on the 
    graphs present in this collection.                                    
    

    SVD-based statistics:
    norm(A)3.051e+06
    min(svd(A))5.19641e-15
    cond(A)5.87137e+20
    rank(A)24,851
    null space dimension330
    full numerical rank?no
    singular value gap25935.3

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

    DIMACS10/ri2010 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.