Does anybody know of an open-source program for computing Tree decomposition of graphs for a fixed "k"(width)? I know that the problem of finding Tree-Decomposition is NP-Hard for variable "k", but my input instances will be really small (~10 nodes) and "k" is fixed.
Some of these software might help you. (Not all of them are open-source though.)
If $n \sim 10$ and $k$ is fixed, then you can even afford to go with an XP algorithm like the one we implemented for our Android app. The source code is here: TreewidthInspector, and for instance with $n \leq 13$ and $k \leq 4$ it terminates in less than a second.
It's approximately 170 lines of code and it's GPL (or MIT or BSD or whatever you should need).
For $n\le150$ you can use the webservice over at http://treedecompositions.com/ to directly obtain and visualize a quick and reasonable decomposition, without having to compile or install anything.
LibTW can still be found. It's at http://www.treewidth.com/treewidth/ .