Over the last year, I've been using Palladio to examine datasets of the Chinese headtax project, which makes it easy to create bivariate network graphs to illustrate relationships between two dimensions. By default, Palladio creates a force-directed layout, which is different from Gephi. Palladio, at the same time, is only limited to this layout. The platform has no way of doing computational or algorithmic analysis of your graphs; you will need a more powerful program like Gephi to do that work. The most powerful method for creating networks come from programming languages such as R, Python, and Javascript. These languages allow you to control various algorithmic and aesthetic aspects of network visualizations. Any dimension of the data can be used as the source and target of a graph.
Regardless, I still find that knowing a bit of each of the data visualization tools would be helpful for any researcher, in any phase of their research process and lifecycle. The following video tutorials is what helps me keep myself informed about not only how to use the tools, but also weighing the strengths and weaknesses of a particular approach to playing around with the data. I'd be interested in hearing how you approach your data. How do you learn the tools of your trade and then decide which would be the best for your own analyses?