I Have been working in some graph theory practical applications like PERT and Simple Line Assembly Balance Problem (Mainly Industrial Engineering topics) and I reached a workflow pretty replicable and comfortable that reduced my graph creation/edit time more than 30%.

Recommended case of use: When the graph you need to create have more than 6 nodes and more than 10 connections.

The tools we need are just a piece of open source software called Yed, it is free and well designed, basically it is a graph editor and diagram tool that will allow us to create our graphs to the import them into Mathematica.

1. Open Yed And create a graph. To change the node label press ENTER and write the name, to change the edge weight do the same with the connection of two nodes. For instance, try the following graph:

1. Go to File menu > Save as... and select GML

2. You can use the import function, however I realized that the weights are not preserved and are turned into edge labels, also the vertex names are not the ones we write in the Yed editor. So I wrote this piece of code to change the properties and match them to the graph editor:

   TransformGML[file_] := Module[
     {g1, rules, vertex, edges, sus},
     g1 = Check[Import[file], Missing];
     vertex = VertexList[g1];
     edges = AnnotationValue[{g1, #}, EdgeLabels] & /@ EdgeRules[g1];
     rules = EdgeRules[g1];
     sus = AnnotationValue[g1, VertexLabels];
     Graph[Replace[#, sus, {1}] & /@ rules, EdgeWeight -> edges, 
      VertexLabels -> Thread[(sus[[All, 1]] /. sus) -> sus[[All, 2]]]]
     ]
   

3. Run calculations into the new graph to verify that it matches the graphical editor:

   WeightedAdjacencyMatrix[g1] // MatrixForm
   
   0   15    20 0   0
   0   0 0   0 30
   0   0 0   5 0
   0   0 0   0 8
   0   0 0   0 0 
   
   Graph[g1, GraphStyle -> "IndexLabeled", EdgeLabels -> "EdgeWeight"]
   

Resulting into the (equivalent) graph:

I hope this may be helpful to someone, also if you have a better way to import external graph created files let me know!