  Temporal Networks, and more specifically, Markovian Temporal Networks,
present a unique challenge regarding the community discovery task. The inherent
dynamism of these systems requires an intricate understanding of memory effects
and structural heterogeneity, which are often key drivers of network evolution.
In this study, we address these aspects by introducing an innovative approach
to community detection, centered around a novel modularity function. We focus
on demonstrating the improvements our new approach brings to a fundamental
aspect of community detection: the detectability threshold problem. We show
that by associating memory directly with nodes' memberships and considering it
in the expression of the modularity, the detectability threshold can be lowered
with respect to cases where memory is not considered, thereby enhancing the
quality of the communities discovered. To validate our approach, we carry out
extensive numerical simulations, assessing the effectiveness of our method in a
controlled setting. Furthermore, we apply our method to real-world data to
underscore its practicality and robustness. This application not only
demonstrates the method's effectiveness but also reveals its capacity to
indirectly tackle additional challenges, such as determining the optimal time
window for aggregating data in dynamic graphs. This illustrates the method's
versatility in addressing complex aspects of temporal network analysis.
