To my (American) ear:
This usage of "given" is very formal. I associate this usage with logic problems like "Given <X>, prove <Y>" or "Given <X>, find <Y>". Thus, "The two given graphs" sounds more natural to me than "The two graphs given" in your usage. I can parse the "The two given graphs…" sentence more easily, because I do not need to check for a construction like "The two graphs, given <these assumptions>,…"
On the other hand, a sentence like "The two graphs were given by Fred to Jane" is grammatical (but not very natural). "The two given graphs from Fred to Jane" is not grammatical.
If the original poster's example is referring to two nearby graphs in the same work, there are other ways to express the idea. These other ways sound more natural to me:
The two graphs show the percentage relationship among UK migrants in the year 2007.
Graph <#1> and graph <#2> show the percentage relationship among UK migrants in the year 2007.
The previous two graphs show the percentage relationship among UK migrants in the year 2007.
The following two graphs show the percentage relationship among UK migrants in the year 2007.
In my second idea, I am trying to reference specific graphs. Sometimes this is done by referencing "Figure 4", or "Step 3", or "Exhibit 29", or "Graph 13", or "Appendix A". Usually the figure will have a more explanatory title, such as "4. Immigrant spouses, by country of origin." or "Graph 13. Relationships of UK immigrants." or "Graph 14: Relationships of UK emigrants."
By the way, I do not know what the original poster means by "the percentage relationship among UK migrants". Also, I am not sure if the graph shows "the percentage relationship among UK migrants", or if it shows something that is affected by (and thus reflects) "the percentage relationship among UK migrants".