I started to work with graph data from Neo4j: http://community.qlik.com/docs/DOC-3115
For visualisation I used Google chart API as you can see in the example application. I also work on an extension for graph display using d3.js and/or raphael lib, but still have some issues.
How have you build the graph chart above? Can you also post some data?
If you think about relationships among customers could be like among products, I think you could consider these two approaches: an Associated Curve chart or a Parallel Coordinates chart.
The Associated Curve chart in this example from QV Design (http://qvdesign.wordpress.com/2012/09/21/informative-curvy-never-before-seen-by-me-at-least-the-associated-curve-chart/) shows relationships among products (sure it could be changed to customers), but the number of elements is fixed. I liked it very much, uses the color intensity to show the relation strength, the buttons (the circles) to select the product in the chart axis, and the associations are created in the script:
The other option is the Parallel Coordinates chart (an example here: http://qvdesign.wordpress.com/2012/01/31/brilliant-qlikview-parallel-co-ordinates-chart/). This option also uses a standard line chart, but the expressions used are complex. I think it would be possible if you could have a Source Customer and a Destination Customer fields:
Hope this helps,