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. 


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


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



I love TikZ. It is a very sophisticated LaTeX package from the same author who wrote Beamer. It takes a bit of getting used to, but once you have your collection of examples, it is extremely efficient and produces very cleanlooking and portable graphics. See www.hairer.org/Archive.zip for a few examples. 


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


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 


Visual Studio has a powerful Directed Graph document (dgml) creator and viewer. It is highly configurable with styles / legend etc. but if you want to generate graphs from a data model it is quite good but there is a bit of a learning curve. I believe (don't quote me on this) that the free versions of Visual Studio do have support for it. Disclaimer: I work on features for Visual Studio close to this; 


Paul Gastin (LSV, Cachan), developed a package named GasTeX in order to simplify graphs and automata designing in TeX. Further informations, documentation and CTAN links on http://www.lsv.enscachan.fr/~gastin/gastex/ Hope it will be of any use. 


GrafEq is light yet usable, it specializes on drawing 'doggy' ones with the lines become really dense. And it's totally free. 

