  Multiple-cluster systems, superclusters, contain large numbers of galaxies
assembled in clusters inter-connected by multi-scale filamentary networks. As
such, superclusters are a smaller version of the cosmic web and can be
considered as miniature universes. Superclusters also contain gas, hot in the
clusters and warmer in the filaments. Thus, they are ideal laboratories to
study the interplay between the galaxies and the gas. In this context, the
Shapley supercluster (SSC) stands out since it hosts the highest number of
galaxies in the local universe. In addition, it is detected in both X-rays and
via the thermal Sunyaev-Zel'dovich (tSZ) effect, making it ideal for a
multi-wavelength study. Applying for the first time a filament-finder based on
graphs, T-REx, on a spectroscopic galaxy catalogue, we uncovered the 3D
filamentary network in and around SSC. Simultaneously, we used a large sample
of photometric galaxies with information on their star formation rates (SFR) in
order to investigate the quenching of star formation in the SSC environments
which we define with the gas distribution in the Planck tSZ map and the ROSAT
X-ray map. We confirm filaments already observed in the distribution of
galaxies of the SSC, and detect new ones. We observe the quenching of star
formation as a function of the gas, and show a general trend of decreasing SFR
where the tSZ and X-ray signals are the highest. Within these regions, we also
observe a rapid decline of the number of star-forming galaxies, coinciding with
an increasing number of transitioning and passive galaxies. Within the
filaments, the fraction of passive galaxies is larger than outside filaments,
irrespective of the gas pressure. Our results suggest the zone of influence of
the SSC, in which galaxies are pre-processed and quenched, is well defined by
the tSZ signal that combines the density and temperature of the environments.
