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To add one more option to the list, I would propose using Commetrix (seee
www.commetrix.de). The tool is a Java-based standalone. 
Its Spring Embedder Layout Algorithm takes into account the strength of
relationships (and also their timing if you coded it) and also displays it
via the different line thickness. 
You can also toggle a slider to interactively change the visualization's
threshold (minimum relationship strength) to literally see how your network
is being reduced/decomposed to its core structure. 
You can add a lot of actor and link attributes to color or filter it more or
to have the relationships colored to represent underlying attributes (i.e.
categories or strength, so that color can additionally be used to see strong
links) and it can also consider the dynamics if your relationships were
developing over time (i.e. events at different time points, it has an
event-based network model).

Greetings,
Matthias Trier.
U Amsterdam/TU Berlin
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