Gephi is the canonical answer for visualization but it can also compute some graph theoretic measures and use it for coloring, sizing etc.
From a tutorial by Paola Tubaro & Yasaman Sarabi:
R packages: SNA, tnet, PNet, RSiena.
*SNA, tnet: metrics, basic models and visualisation;
*PNet for ERGM (cross-section modeling);
*RSiena for longitudinal data modeling (SAOM);
*More difficult at the beginning, but more powerful and versatile; Freely available.
UCINET and Netdraw
*For data management, metrics, basic models, and visualisation.
*Easy to use, widely used; Comprehensive tutorial available on the web, good Help function; Free for one-month trial, then needs to be purchased.
Pajek
*For exploratory data analysis and visualisation; Good for large networks, widely used; Some tutorials available on the web, a support book; Freely available online.
I agree: Gephi is the best... Take care of the operative system that you have in you PC or MAC. With the last version of the OS for Mac, i have some problems in working with Gephi. But the output are really very good.. less from the point of view of the statistical analysis. But you can use Ucinet for this.
I've used SPSS Modeler. Its absolutely awesome to say the least.
Takes a while to orient yourself to how decision trees work on IBM SPSS Modeler, but when you do, its very heuristic! It allows you to input data in various forms. Lets you compare data in different forms and the decision trees are interesting to make interesting conversations. I was able to visualize my data/decisions in many ways. I found it very useful.
Jiang B. (2015), Head/tail breaks for visualization of city structure and dynamics, Cities, 43, 69-77, Preprint: http://arxiv.org/ftp/arxiv/papers/1501/1501.03046.pdf
Jiang B. and Miao Y. (2014), The evolution of natural cities from the perspective of location-based social media, The Professional Geographer, xx(xx), xx-xx, DOI: 10.1080/00330124.2014.968886, Preprint: http://arxiv.org/abs/1401.6756
Jiang B., Duan Y., Lu F., Yang T. and Zhao J. (2014), Topological structure of urban street networks from the perspective of degree correlations, Environment and Planning B: Planning and Design, 41(5), 813-828.