  In this study, we present a general framework for comparing two dynamical
processes that describe the synchronization of oscillators coupled through
networks of the same size. We introduce a measure of dissimilarity defined in
terms of a metric on a hypertorus, allowing us to compare the phases of coupled
oscillators. In the first part, this formalism is implemented to examine
systems of networked identical phase oscillators that evolve with the Kuramoto
model. In particular, we analyze the effect of the weight of an edge in the
synchronization of two oscillators, the introduction of new sets of edges in
interacting cycles, the effect of bias in the couplings, and the addition of a
link in a ring. We also compare the synchronization of nonisomorphic graphs
with four nodes. Finally, we explore the dissimilarities generated when we
contrast the Kuramoto model with its linear approximation for different random
initial phases in deterministic and random networks. The approach introduced
provides a general tool for comparing synchronization processes on networks,
allowing us to understand the dynamics of a complex system as a consequence of
the coupling structure and the processes that can occur in it.
