Vpeljemo modificirani Hosoyev polinom dvojno uteženih grafov, tj. povezavno in vozliščno uteženih grafov, ki omogoča izpeljavo zaključenih izrazov za Hosoyev polinom nekaterih posebnih grafov ...vključno z enocikličnimi grafi. Nadalje, Hosoyev polinom zapišemo kot vsoto povezavnih prispevkov, kar predstavlja posplošitev dobro znanih analognih rezultatov za Wienerjev indeks. Podamo linearen algoritem za računanje Hosoyevega polinoma na kaktusnih grafih. Hosoyev polinom obširno preučujejo v kemijski teoriji grafov, njegove utežene različice pa imajo zanimive uporabe v teoriji komunikacijskih omrežij.
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