**Matrix: SNAP/ca-GrQc**

Description: Collaboration network of Arxiv General Relativity

(undirected graph drawing) |

Matrix properties | |

number of rows | 5,242 |

number of columns | 5,242 |

nonzeros | 28,980 |

# strongly connected comp. | 355 |

explicit zero entries | 0 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | binary |

structure | symmetric |

Cholesky candidate? | no |

positive definite? | no |

author | J. Leskovec, J. Kleinberg and C. Faloutsos |

editor | J. Leskovec |

date | 2003 |

kind | undirected graph |

2D/3D problem? | no |

Additional fields | size and type |

nodename | full 5242-by-1 |

Notes:

Networks from SNAP (Stanford Network Analysis Platform) Network Data Sets, Jure Leskovec http://snap.stanford.edu/data/index.html email jure at cs.stanford.edu 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. Files File Description ca-GrQc.txt.gz Collaboration network of Arxiv General Relativity category

SVD-based statistics: | |

norm(A) | 45.6167 |

min(svd(A)) | 0 |

cond(A) | Inf |

rank(A) | 4,804 |

null space dimension | 438 |

full numerical rank? | no |

singular value gap | 3.88298e+11 |

singular values (MAT file): | click here |

SVD method used: | s = svd (full (A)) ; |

status: | ok |

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.
*