MATLAB. Unlike CASs (Mathematica & Maple are the most popular), and unlike statistical software packages like R, SAS, etc., MATLAB is designed with modeling, computational analyses, etc., from the ground up (after all, the name comes from "matrix laboratory", so it is designed for multivariable/multivariate mathematics even without the extras it offers) and it comes with toolboxes for systems modelling, tools for dealing with complexity, etc. However, it is as far from open source as one can get. R is free, but isn't as ideal here (it's too oriented towards statistics).

For open source, there's sage (see link below). Sage was designed to create "a viable free open source alternative to Magma, Maple, Mathematica and Matlab." It incorporates other open source solutions like Numpy, Scipy, NetworkX, Ipython, etc. (see second link below).

http://sagemath.org/

http://sagemath.org/links-components.html

Have you tried specialized software like Wolfram Mathematica? 

It provides great programming language and exellent interactive presentation layer.

http://demonstrations.wolfram.com/DynamicalNetworkDesignForControllingVirusSpread/ 

I agree with Dr. Guzev, Mathematica is a great software for that kind of aplications, however if you have some budget limitatios you can try IPython, this python disttribution alredy have installed some scientific computing packages as well as some networks analysis packages

http://ipython.org/

http://nbviewer.ipython.org/github/dboyliao/cookbook-code/blob/master/notebooks/chapter06_viz/04_d3.ipynb

I used a litle bit of Mathematica to Cellular Automata and it works very fine. But I did not use it to graphs. I will try.

I will see about ipython too.

Thank you for your answers.

MATLAB. Unlike CASs (Mathematica & Maple are the most popular), and unlike statistical software packages like R, SAS, etc., MATLAB is designed with modeling, computational analyses, etc., from the ground up (after all, the name comes from "matrix laboratory", so it is designed for multivariable/multivariate mathematics even without the extras it offers) and it comes with toolboxes for systems modelling, tools for dealing with complexity, etc. However, it is as far from open source as one can get. R is free, but isn't as ideal here (it's too oriented towards statistics).

For open source, there's sage (see link below). Sage was designed to create "a viable free open source alternative to Magma, Maple, Mathematica and Matlab." It incorporates other open source solutions like Numpy, Scipy, NetworkX, Ipython, etc. (see second link below).

http://sagemath.org/

http://sagemath.org/links-components.html

for stimulating various network parameter you can use NS2 or NS3

graphlab is based on graph-centered computation for machine learning.  I would imagine that it could be used for the kind of problem you are considering.

The SNAP library from Stanford might be a good way to go if you're happy working with low-level languages - hopefully you might find a binding for java?  Alternatively, R has so good nework tools.

I'll also suggest Python for scientific computing (check the links below for reasons). For complex networks there is the Python NetworkX library that may help you. If simulations will be a core part of your study though you may also consider using an ABMS platform like Netlogo or RePast.

http://www.talyarkoni.org/blog/2013/11/18/the-homogenization-of-scientific-computing-or-why-python-is-steadily-eating-other-languages-lunch/

https://metarabbit.wordpress.com/2013/10/18/why-python-is-better-than-matlab-for-scientific-software/

http://cyrille.rossant.net/why-using-python-for-scientific-computing/

The iGraph package for C and Python do great if you have coding skills.

http://igraph.org/python/

Yes I believe Python is used to model complex systems. There are several examples in the systems modeling literature

Python is great

If you're looking for free software to generate network descriptive statistics (average path length, betweenness centrality, GSCC, etc....), I would highly recommend the igraph package for C, Python, or R.  It's fairly straightforward to use and can be easily integrated into disease simulation models written in those languages.

Python is ideal, if you want an open source platform, otherwise Matlab is more useful in complex network analysis.

Python is used to model complex systems. If you're looking for free software to generate network descriptive statistics Python is ideal, if you want an open source platform, otherwise Matlab is more useful in complex network analysis.

Depends on your purposes

For small networks (lesser than 100.000 nodes)

* Python: because have the networkx and igraph library

For several statistical analysis:

* R: because have several libraries of statistics and have too the igraph library

For intensive calculus in very large networks:

* C/C++: for very huge networks, because is fast and have the igraph library.