Rome's Three Heirs Connections Question

Arguably, each of these three civilizations could claim the mantle of the Roman Empire. In your view, which one has the strongest claim to carrying forward the legacies of the classical past?

       The three civilizations that came after Rome, the Byzantines, Islam, and Northwestern Rome, were uniquely related to Rome in their own ways. The author of Western Civilizations tells that Byzantium had a stronger focus on legal and political institutions, Islam continued the trade and cultural exchange that Rome had started, and Northwestern Europe associated itself with Rome in that it carried the Latin language, the city of Rome, and its Christian patriarchy. So the question in order is which of these criteria more embodied the nation of Rome and its values as a whole.
       In my view, Rome is better defined, out of these characteristics, by the values of Northwest Europe. The city of Rome was the headquarters and origin of Rome itself so the fact that Northwest Europe identified with the city of Rome shows their connection to the true base of Rome. However, what distinguishes Northwest Rome as more Roman than the others is its connection to the Christian Patriarchal system. This was a system that came about with the emergence of Christianity in Rome during the time of Constantinople. Rome instituted many political reforms because of Christianity, so it became an integrated part of their government. So, since Northwest Europe had this Christian Patriarchal system, it gives their government a distinguishing characteristic that Rome had and other civilizations did not.