[igraph] representation large networks with edge and nodes features

[Leonardo Mazzoni]

Hi everybody,
I need to represent a large matrix with the following features.
It is a  symmetric 562x562 matrix composed by decimal values that goes 
from 0 to 1 and I would like to represent its maximum spanning tree 
(with the function mst, weighting for the negative values) with the 
following features:

1) assign quantitative attributes to nodes, shaping their size (setting 
a scale) and creating the correspondent legend
2) assign qualitative attributes to nodes, defining their colour 
(setting correspondent category) and creating the correspondent legend

Then, the representation of my networks should be like these:
a) represent first a graph with the chacateristics of point 1 and 2 with 
the edge values (that go from 0 to 1) with only the values bigger than a 
certain threshold of relationship (e.g. bigger than 0.3);
b) represent a second graph  with the chacateristics of point 1 and 2 
with all the edge values, assigning diverse colours to diverse level of 
intensity of the relationship (from 0.1 to 0.2, from 0.2 to 0.3,etc..).

I tried to do something, but I stopped, looking at the incomprehensible 
graph that I produced..
I forward my first attempt to do it with i-graph:

g <- graph_from_adjacency_matrix(foo, mode = "upper", weighted = T, diag 
= F)
max_spann_tree <- mst(g, weights = -E(g)$weight)
plot.igraph(max_spann_tree,vertex.label=V(net)$name, 
vertex.attibutes=V(net), 
edge.color="grey",vertex.color="red",edge.attributes=E(g)$weight,layout=layout.spring)

Any suggestions to do it in igraph?
In the attachment there is a picture of the Product Space by Hidalgo et 
al. (2007), that is more or less the picture I would like to get.
https://www.google.com/search?q=the+product+space+hidalgo&client=firefox-b-ab&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjOiNu5lbLbAhWIcRQKHV5VCSIQ_AUICigB&biw=1366&bih=654#imgrc=FeSyfj9wjHcVnM:

Many thanks in advance!

Regards

TheProductSpace.png
Description: PNG image