Exposure to fine particles (PM10) has adverse health effects. In partnership with the University of Córdoba and the University of the Antilles, the KaruSphere laboratory studied the stochastic behavior of PM10 time series using a complex network framework. In this study, the method known as Visibility Graph (VG, visibility graph) is used to describe the dynamics of PM10 in the Guadeloupe archipelago. First, the fractal nature of the PM10 time series is highlighted using the degree distribution for all data, low dust season (October to April) and high dust season (May to September). Subsequently, an in-depth description of the PM10 dynamics is made using a multifractal analysis through two approaches, namely the Rényi spectrum and the singularity spectrum. The results obtained are consistent with the behavior of PM10 in the Caribbean basin. Both methods showed a higher degree of multifractality during the low dust season. Moreover, the multifractal parameters showed that the low season has the highest degree of recurrence and a lower degree of uniformity. Finally, centrality measurements (degree, proximity and interference) highlighted the dynamics of PM10 throughout the year with a decrease in centrality values during the high dust season.