**Matrix: Newman/power**

Description: Western States Power Grid, Watts & Strogatz

(undirected graph drawing) |

Matrix properties | |

number of rows | 4,941 |

number of columns | 4,941 |

nonzeros | 13,188 |

# strongly connected comp. | 1 |

explicit zero entries | 0 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | binary |

structure | symmetric |

Cholesky candidate? | no |

positive definite? | no |

author | D. Watts, S. Strogatz |

editor | M. Newman |

date | 1998 |

kind | undirected graph |

2D/3D problem? | no |

Notes:

Network collection from M. Newman http://www-personal.umich.edu/~mejn/netdata/ Western States Power Grid Compiled by Duncan Watts and Steven Strogatz The graph "power" contains an undirected unweighted representation of the topology of the Western States Power Grid of the United States, compiled by Duncan Watts and Steven Strogatz. The data are from the web site of Prof. Duncan Watts at Columbia University, http://cdg.columbia.edu/cdg/datasets. Node IDs are the same as those used by Prof. Watts. These data can be cited as: D. J. Watts and S. H. Strogatz, "Collective dynamics of `small-world networks", Nature 393, 440-442 (1998). Note by Tim Davis: this graph has the same number of nodes and edges as the Pajek/USpowerGrid graph. They are related as follows: Prob1 = UFget ('Newman/power') Prob2 = UFget ('Pajek/USpowerGrid') A = Prob1.A ; B = Prob2.B ; n = size (A,1) ; p = [2:n 1] ; isequal (A (p,p), B) This is because of the way the Pajek data set converted 0-based node IDs to 1-based. In the Pajek set, node 0 is renamed node n, and this translation was then imported into the Pajek/ Group in the UF collection. The standard convention in MATLAB, and (elsewhere) in the UF Collection, is to map nodes 0:n-1 of a zero-based graph to 1:n. The latter translation preserves the relative numbering of all the nodes; the Pajek translation does not. Although technically Newman/power is a duplicate matrix, I have added it to the UF Collection to preserve the original relative node ordering.

SVD-based statistics: | |

norm(A) | 7.48305 |

min(svd(A)) | 3.10852e-19 |

cond(A) | 2.40727e+19 |

rank(A) | 4,348 |

null space dimension | 593 |

full numerical rank? | no |

singular value gap | 2.23267e+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.
*