Complex network theory is used to analyze the spatiotemporal dynamics of the PRECCINSTA swirl burner, operating on hydrogen-methane fuel blends. At a power setting of 15 kW with equivalence ratio of 0.8 and hydrogen fuel fraction (HFF) ranging from 0% to 80%, period-1 and period-2 limit cycle oscillations as well as chaotic oscillations were observed. A turbulence network was constructed from the vorticity data obtained with particle image velocimetry. In addition, a heat release rate (HRR) correlation network was constructed from chemiluminescence images. Although the two networks concern a common thermoacoustic system, both exhibit significant differences: the turbulence network displays power law degree distribution, maintains small world property for all HFFs and is scale-free only in the absence of hydrogen enrichment. The HRR correlation network does not feature these properties, but hints at an asymmetric coupling between the heat release rate and the acoustic pressure for all HFFs. Furthermore, the HRR network is responsive to changes in HFF and the corresponding shifts in the dynamical state as well as in the root-mean-square of acoustic pressure. On the contrary, the turbulence network displays no such sensitivity and its properties are almost constant in the upper HFF range. It exhibits stationary hub structures for all the fuel blends tested, whereas the HRR correlation network is hub-free. © 2022 Elsevier Inc. All rights reserved.