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Plot network with edges depending on weights?

I have the following weights and graph:

w = {2., 1., 0.5, 0.3, 1.2};
GraphPlot[{1 -> 2, 3 -> 1, 3 -> 2, 4 -> 1, 4 -> 2}]

What I want is to visualize the graph in such a way that edges have a different thickness and color proportionally, depending on the weights given.

Does anyone know how to do this in Mathematica?

Thanks in advance for any help!
POSTED BY: David G. Aragonés
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I wrote a little guide that might be useful to you: On design of styles for small weighted graphs

https://community.wolfram.com/groups/-/m/t/838652

enter image description here
POSTED BY: Vitaliy Kaurov
POSTED BY: Szabolcs Horvát

Amazing answer!

Thank you so much!

I've done some work over your code to reach this:

Networks

I hope your answer can be helpful also for other people =)
POSTED BY: David G. Aragonés
POSTED BY: Seth Chandler

I would recommend using the newer Graph method rather than the older GraphPlot. I've made up some functions for thickness and coloring. You will want to use your own.

  w = {2., 1., 0.5, 0.3, 1.2};
  g = Graph[{1 -> 2, 3 -> 1, 3 -> 2, 4 -> 1, 4 -> 2}];
  styledEdges = MapThread[
   Property[#1, 
     EdgeStyle -> {Hue[LogisticSigmoid[#2]], 
       Thickness[Min[0.03, #2/100]]}] &, {EdgeList[g], w}];
 Graph[styledEdges]
POSTED BY: Seth Chandler
POSTED BY: David G. Aragonés
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