Matrix: SNAP/ca-GrQc

Description: Collaboration network of Arxiv General Relativity

SNAP/ca-GrQc graph
(undirected graph drawing)

scc of SNAP/ca-GrQc

  • Home page of the UF Sparse Matrix Collection
  • Matrix group: SNAP
  • Click here for a description of the SNAP group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups
  • download as a MATLAB mat-file, file size: 76 KB. Use UFget(2297) or UFget('SNAP/ca-GrQc') in MATLAB.
  • download in Matrix Market format, file size: 63 KB.
  • download in Rutherford/Boeing format, file size: 48 KB.

    Matrix properties
    number of rows5,242
    number of columns5,242
    # strongly connected comp.355
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

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

    Additional fieldssize and type
    nodenamefull 5242-by-1


    Networks from SNAP (Stanford Network Analysis Platform) Network Data Sets,     
    Jure Leskovec                         
    email jure at                                                  
    General Relativity and Quantum Cosmology collaboration network                 
    Dataset information                                                            
    Arxiv GR-QC (General Relativity and Quantum Cosmology) collaboration network is
    from the e-print arXiv and covers scientific collaborations between authors    
    papers submitted to General Relativity and Quantum Cosmology category. If an   
    author i co-authored a paper with author j, the graph contains a undirected    
    edge from i to j. If the paper is co-authored by k authors this generates a    
    completely connected (sub)graph on k nodes.                                    
    The data covers papers in the period from January 1993 to April 2003 (124      
    months). It begins within a few months of the inception of the arXiv, and thus 
    represents essentially the complete history of its GR-QC section.              
    Dataset statistics                                                             
    Nodes   5242                                                                   
    Edges   28980                                                                  
    Nodes in largest WCC    4158 (0.793)                                           
    Edges in largest WCC    26850 (0.927)                                          
    Nodes in largest SCC    4158 (0.793)                                           
    Edges in largest SCC    26850 (0.927)                                          
    Average clustering coefficient  0.5296                                         
    Number of triangles     48260                                                  
    Fraction of closed triangles    0.6298                                         
    Diameter (longest shortest path)    17                                         
    90-percentile effective diameter    7.6                                        
    Source (citation)                                                              
    J. Leskovec, J. Kleinberg and C. Faloutsos. Graph Evolution: Densification and 
    Shrinking Diameters. ACM Transactions on Knowledge Discovery from Data (ACM    
    TKDD), 1(1), 2007.                                                             
    File    Description                                                            
    ca-GrQc.txt.gz  Collaboration network of Arxiv General Relativity category     

    SVD-based statistics:
    null space dimension438
    full numerical rank?no
    singular value gap3.88298e+11

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

    SNAP/ca-GrQc 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.