?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F2805%2F&rft.title=Generalized+Erdos+Numbers+for+network+analysis&rft.creator=Morrison%2C+Greg&rft.creator=Dudte%2C+Levi&rft.creator=Mahadevan%2C+L.&rft.subject=H+Social+Sciences+(General)&rft.subject=QC+Physics&rft.description=In+this+paper+we+consider+the+concept+of+%60closeness'+between+nodes+in+a+weighted+network+that+can+be+defined+topologically+even+in+the+absence+of+a+metric.+The+Generalized+Erd%5CH%7Bo%7Ds+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%2C+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%2C+and+we+use+a+linearized+form+of+the+GENs+to+develop+a+continuum+model+for+%60closeness'+in+spatial+networks.+As+an+example+of+their+practicality%2C+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.&rft.publisher=arXiv&rft.date=2015-07&rft.type=Working+Paper&rft.type=PeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.rights=cc_by_nc&rft.identifier=http%3A%2F%2Feprints.imtlucca.it%2F2805%2F1%2Fgeneralized.pdf&rft.identifier=++Morrison%2C+Greg+and+Dudte%2C+Levi+and+Mahadevan%2C+L.++Generalized+Erdos+Numbers+for+network+analysis.++Working+Paper+++arXiv+++++++(Submitted)+++&rft.relation=http%3A%2F%2Farxiv.org%2Fabs%2F1507.04400