## 2 Materials and Methods  
Suspensions of few-layered graphene nanoparticles (FLG) were manufactured via a previously described [47] direct ultrasonic-assisted liquid-phase exfoliation route in deionized water with a fluorine-containing surfactant (Zonyl BA-L, Dupont, Wilmington, DE, USA). Natural graphite (GSM-2 brand) was used as a precursor. Graphite was heat-treated under vacuum at 2100 \({}^{\circ}\)C followed by high-temperature (2800 \({}^{\circ}\)C) treatment in a Freon R22 atmosphere in order to obtain >99.9 wt.% purity. Ultrasonication time was 6 h in all cases. A horn-type unit with acoustic power 200 W was used.  
AgNPs were manufactured via polyol synthesis following the protocol described in [48]. Synthesis temperature was kept at 170 \({}^{\circ}\)C. Silver nitrate (extra pure 99.9+%, Lenreactiv, St. Petersburg, Russia), potassium bromide (99.9+%, Acros Organics, Geel, Belgium), ethylene glycol (EG) (extra pure, Acros Organics, Geel, Belgium) were used as precursors, whereas surface stabilizer polyvinylpyrrolidone (PVP) of low (M\({}_{w}\) 8000, 99.995+% pure, Acros Organics, Geel, Belgium) molecular weightwas used. The PVP:AgNO\({}_{3}\) weight ratio was kept at 5:2. Synthesis was carried out in air.  
In order to obtain transparent conductive suspensions, an EBA 280 centrifuge (Hettich, Beverly, MA, USA) was used, operating at cycles at 2000 rpm (whenever not specified, total centrifugation time was 30 min). Before centrifugation, each suspension was treated with ultrasound using a horn-type ultrasonication device (MEF391, Melfiz, Russia) for 10 min to ensure homogeneity of the probe, as was concluded from the stability of particle size distributions in a series of probes. After each cycle, fugate was separated and, after analysis, used for further treatment. The sediment was rinsed with acetone (99.5+%, Ecos-1, Russia), dried at 100 \({}^{\circ}\)C and weighed (Ohaushaus P224/E, Ohaus, Parsippany, NJ, USA) in order to calculate and correct concentrations. Sufficiently centrifuged suspensions were transparent and yellow in colour. Residual concentration was estimated by carefully measuring the mass of the sediment. Hybrid suspensions were prepared by simple mixing of graphene aqueous suspensions and AgNP suspension in EG followed by ultrasonication for 15 min to ensure homogeneity and reduce agglomeration.  
Particle-size distributions for un-centrifuged suspensions were measured via a laser diffraction (ISO 13320:2020) technique using Microtrac MRB SYNC apparatus (Microtrac, Osaka, Japan). For centrifuged suspensions, distributions were obtained via dynamic laser scattering (Nanosizer, Malvern Pananalytical, Malvern, UK). Quartz cuvettes were used for measurements (optical path length 10 mm).  
Electrical conductivity measurements were performed with a SevenCompact conductometer equipped with InLab 710 glass/platinum electrodes (Mettler Toledo, Greifensee, Switzerland); 20 mL aliquots of suspensions were used. Sheet resistance was estimated via an IEC/TS 62607-2-1-2017-compatible 4-electrode method. We used copper electrodes and a b2901a precision source/measure unit (Keysight, Santa Rosa, CA, USA). Films were drop-casted (F1-ClipTip GLP, Thermo Scientific, Waltham, MA, USA) on glass substrates, and sintering was performed at 150 \({}^{\circ}\)C. Resistance was calculated from V-I curves (linear region slope at 0 V).  
Optical spectra were recorded using a Cary 60 UV-vis spectrometer (Agilent, Santa Clara, CA, USA). All spectra were plotted for the 200-1100 nm range at 0.4 nm wavelength resolution. All as-synthesized suspensions were diluted 100 times in order to decrease absorption, while centrifuged suspensions were used as prepared. Quartz cuvettes were used for measurements (optical path length 10 mm).  
TEM images were taken using a HT7800 (Hitachi, Tokyo, Japan) unit operating at a 100 kV accelerating voltage. SEM images were obtained using TM4000 unit (Hitachi, Japan) at 15 kV accelerating voltage.