Morrison, Greg and Mahadevan, L.
*Asymmetric network connectivity using weighted harmonic averages.*
EPL (Europhysics Letters), 93 (4).
p. 40002.
ISSN 0295-5075
(2011)

## Abstract

We propose a non-metric measure of the "closeness" felt between two nodes in an undirected, weighted graph using a simple weighted harmonic average of connectivity, that is a real-valued Generalized Erdös Number (GEN). While our measure is developed with a collaborative network in mind, the approach can be of use in a variety of artificial and real-world networks. We are able to distinguish between network topologies that standard distance metrics view as identical, and use our measure to study some simple analytically tractable networks. We show how this might be used to look at asymmetry in authorship networks such as those that inspired the integer Erdös numbers in mathematical coauthorships. We also show the utility of our approach to devise a ratings scheme that we apply to the data from the NetFlix prize, and find a significant improvement using our method over a baseline.

Item Type: | Article |
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Identification Number: | 10.1209/0295-5075/93/40002 |

Uncontrolled Keywords: | Mathematical physics - PACS: 02.10.Ox Combinatorics; graph theory |

Subjects: | Q Science > QA Mathematics Q Science > QC Physics |

Research Area: | Economics and Institutional Change |

Depositing User: | Ms T. Iannizzi |

Date Deposited: | 04 Oct 2013 10:20 |

Last Modified: | 04 Oct 2013 10:20 |

URI: | http://eprints.imtlucca.it/id/eprint/1824 |

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