eprintid: 2805
rev_number: 10
eprint_status: archive
userid: 69
dir: disk0/00/00/28/05
datestamp: 2015-11-03 10:10:07
lastmod: 2015-11-03 10:10:07
status_changed: 2015-11-03 10:10:07
type: monograph
metadata_visibility: show
creators_name: Morrison, Greg
creators_name: Dudte, Levi
creators_name: Mahadevan, L.
creators_id: greg.morrison@imtlucca.it
creators_id: 
creators_id: 
title: Generalized Erdos Numbers for network analysis
ispublished: submitted
subjects: H1
subjects: QC
divisions: EIC
full_text_status: public
monograph_type: working_paper
keywords: Physics and Society, Social and Information Networks
abstract: In this paper we consider the concept of `closeness' between nodes in a weighted network that can be defined topologically even in the absence of a metric. The Generalized Erd\H{o}s Numbers (GENs) satisfy a number of desirable properties as a measure of topological closeness when nodes share a finite resource between nodes as they are real-valued and non-local, and can be used to create an asymmetric matrix of connectivities. We show that they can be used to define a personalized measure of the importance of nodes in a network with a natural interpretation that leads to a new global measure of centrality and is highly correlated with Page Rank. The relative asymmetry of the GENs (due to their non-metric definition) is linked also to the asymmetry in the mean first passage time between nodes in a random walk, and we use a linearized form of the GENs to develop a continuum model for `closeness' in spatial networks. As an example of their practicality, we deploy them to characterize the structure of static networks and show how it relates to dynamics on networks in such situations as the spread of an epidemic.
date: 2015-07
date_type: published
publication: arXiv
publisher: arXiv
pages: 39
institution: IMT Institute for Advanced Studies Lucca
refereed: TRUE
official_url: http://arxiv.org/abs/1507.04400
citation:   Morrison, Greg and Dudte, Levi and Mahadevan, L.  Generalized Erdos Numbers for network analysis.  Working Paper   arXiv       (Submitted)   
document_url: http://eprints.imtlucca.it/2805/1/generalized.pdf