**Matrix: SNAP/p2p-Gnutella05**

Description: Gnutella peer to peer network from August 5 2002

(bipartite graph drawing) | (graph drawing of A+A') |

Matrix properties | |

number of rows | 8,846 |

number of columns | 8,846 |

nonzeros | 31,839 |

# strongly connected comp. | 5,613 |

explicit zero entries | 0 |

nonzero pattern symmetry | 0% |

numeric value symmetry | 0% |

type | binary |

structure | unsymmetric |

Cholesky candidate? | no |

positive definite? | no |

author | M. Ripeanu and I. Foster and A. Iamnitchi |

editor | J. Leskovec |

date | 2002 |

kind | directed graph |

2D/3D problem? | no |

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 Gnutella peer-to-peer network, August 5 2002 Dataset information A sequence of snapshots of the Gnutella peer-to-peer file sharing network from August 2002. There are total of 9 snapshots of Gnutella network collected in August 2002. Nodes represent hosts in the Gnutella network topology and edges represent connections between the Gnutella hosts. Dataset statistics Nodes 8846 Edges 31839 Nodes in largest WCC 8842 (1.000) Edges in largest WCC 31837 (1.000) Nodes in largest SCC 3234 (0.366) Edges in largest SCC 13453 (0.423) Average clustering coefficient 0.0093 Number of triangles 1112 Fraction of closed triangles 0.007598 Diameter (longest shortest path) 9 90-percentile effective diameter 5.3 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. M. Ripeanu and I. Foster and A. Iamnitchi. Mapping the Gnutella Network: Properties of Large-Scale Peer-to-Peer Systems and Implications for System Design. IEEE Internet Computing Journal, 2002. Files File Description p2p-Gnutella05.txt.gz Directed Gnutella P2P network from August 5 2002

SVD-based statistics: | |

norm(A) | 21.4205 |

min(svd(A)) | 0 |

cond(A) | Inf |

rank(A) | 3,734 |

null space dimension | 5,112 |

full numerical rank? | no |

singular value gap | 1.24812e+12 |

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.
*