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13.
Relative edge betweenness centrality
Vukičević, Damir ; Škrekovski, Riste ; Tepeh, Aleksandra
Vpeljemo novo povezavno središčno mero - relativno povezavno vmesnost ▫$\gamma (uv) = b(uv)/\sqrt{c(u)c(v)}$▫, kjer je ▫$b(uv)$▫ standardna povezavna vmesnost, ▫$c(u)$▫ pa uravnana vozliščna ...vmesnost. V tej alternativni definiciji je pomembnost povezave normalizirana glede na pomembnost njenih krajišč. To da boljšo predstavitev ''lokalne'' pomembnosti povezave, tj. njene pomembnosti v bližnji okolici. Podamo natančne spodnje in zgornje meje za to invarianto skupaj s karakterizacijo grafov, ki dosežejo te meje. Poleg tega obravnavamo meje za različne zanimive družine grafov, navedemo pa tudi nekaj odprtih problemov.
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