Hi, does anyone know of a good program for drawing directed weighted graphs?
Thanks

Try Sage  it's open source and can draw weighted directed graphs. For example:



Try Graphviz  it's open source and quite flexible as far as usage is concerned. It's good at automatic layouts etc, where for example Maple would make a mess of things. 


Check out PGF/tikZ, which is freely available, and interacts extremely well with TeX and LaTeX. You can find examples here, examples of graphs here, and a nice manual here. A nice feature of the examples web page is that you can click on each example to get access to the code, which you can then copyandpaste into your own LaTeX file, and then modify for your own purposes. 


To supplement William Stein's useful answer, here is a graph produced by running the code he
displays:



Mathematica is quite good these days and exports in a bazillion formats. 


you can use $newgraph1.1.3$ for drawing and analysis every graphs. It is very good free software. 


Very simple, and easy to use for small graphs: GraphThing. It is in Ubuntu repositories. Here is home page: http://graph.seul.org/ It even computes some simple parameters. 


I have used CaGe for some basic planar graphs. 


https://networkx.lanl.gov/trac has a lot of options 


Try programming in R for various types of Graphs and Data Analysis. The R Graphs Cookbook is an essential. You'll find it here. 

