Ok, so I figured it out myself, and I will leave the details here to help anyone with the same questions.
Graph of one color with labels on nodes:
This will create a graph similar to the one asked for the question, with lines connecting the circles with the labels inside.

plot 'edges.dat' u 1:2 with lines lc rgb "black" lw 2 notitle,\ 'edges.dat' u 1:2:(0.6) with circles fill solid lc rgb "black" notitle,\ 'edges.dat' using 1:2:($0) with labels tc rgb "white" offset (0,0) font 'Arial Bold' notitle
With minor changes, it can be compared with the image of the question.

plot 'edges.dat' u 1:2 with lines lc rgb "black" lw 2 notitle,\ 'edges.dat' u 1:2:(0.8) with circles linecolor rgb "white" lw 2 fill solid border lc lt 0 notitle, \ 'edges.dat' using 1:2:($0) with labels offset (0,0) font 'Arial Bold' notitle
Cluster color graph:

unset colorbox set palette model RGB defined ( 0 0 0 0 , 1 1 0 0 , 2 1 0.9 0, 3 0 1 0, 4 0 1 1 , 5 0 0 1 , 6 1 0 1 ) plot 'edges.dat' u 1:2:3 with lines lc palette notitle,\ 'edges.dat' u 1:2:(0.15):3 with circles fill solid palette notitle
The data used on all graphs follows this structure:
21.53 9.55 0 24.26 7.92 0 5.63 3.23 1 2.65 1.77 1 5.63 3.23 0 4.27 7.04 0 (...)
rgcalsaverini
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