Different sensitivity tests can be used to test the AHP outcomes, each test has it own features, methodology and steps, therefore you need to perform it gradually to check the effect of change on the outcomes, in most cases Excel sheets are enough and can serve the purpose, in other cases you need to build your own 'software' MATLAB is excellent.
You should use software "Expert choice". In this software you can perform all type of sensitivity analysis and plot graphs also. Further you should read my article "Vinod Yadav Milind Kumar Sharma , (2016),"Multi-criteria supplier selection model using the analytic hierarchy process approach", Journal of Modelling in Management, Vol. 11 Iss 1 pp. 326 - 354".
You could also use SuperDecisions software of the Creative Decisions Foundation. Select the Computations Sensitivity command to get into the sensitivity module. It is necessary to set the independent variable to see a meaningful sensitivity graph. There is one line for each alternative in sensitivity windows. In the software they are color coded so that it is easy to see which line corresponds to each alternative.
I tried doing it in excel sheet. but the final result did not help me in interpreting my objective. My objective is to see the effect on the other variables if one variable's eigen vector is altered. Kindly help.
I have been working with AHP for more than 10 yearsm dealing with a lot of situations.
There are many softwares you can use, but in my modest opinion, the best way is model it in a MS-Excel or LibreOffice-Calc sheet (or Matlab or Scilab), because the modelling process is a ooportunity to understand the problem better.
After that, it is a procedure you can permorf to understand results.
I don't know if there is a software to do that, but if there were, it wouldn't be a good idea to believe in it. A research in command is better then automated procedures.
I recommend you to use the SuperDecisions like Yousef did. You can find it http://www.superdecisions.com/.
Please have a look at its patents too. When you read the patents and reference documents of the SuperDecisions you will find many details of the Sensitivity Analysis.
For some other types of Sensitivity Analysis based on some research papers you should contact to the authors or you have to develop your own tools on Excel, Calc, Scilab, R. Octave and so forth.