**Matrix: SNAP/ca-HepTh**

Description: Collaboration network of Arxiv High Energy Physics Theory

(undirected graph drawing) |

Matrix properties | |

number of rows | 9,877 |

number of columns | 9,877 |

nonzeros | 51,971 |

# strongly connected comp. | 429 |

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 9877-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 High Energy Physics - Theory collaboration network Dataset information Arxiv HEP-TH (High Energy Physics - Theory) collaboration network is from the e-print arXiv and covers scientific collaborations between authors papers submitted to High Energy Physics - Theory 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 HEP-TH section. Dataset statistics Nodes 9877 Edges 51971 Nodes in largest WCC 8638 (0.875) Edges in largest WCC 49633 (0.955) Nodes in largest SCC 8638 (0.875) Edges in largest SCC 49633 (0.955) Average clustering coefficient 0.4714 Number of triangles 28339 Fraction of closed triangles 0.284 Diameter (longest shortest path) 17 90-percentile effective diameter 7.5 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-HepTh.txt.gz Collaboration network of Arxiv High Energy Physics Theory category

SVD-based statistics: | |

norm(A) | 31.0348 |

min(svd(A)) | 3.17278e-43 |

cond(A) | 9.7816e+43 |

rank(A) | 9,040 |

null space dimension | 837 |

full numerical rank? | no |

singular value gap | 2.85526e+10 |

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.
*