Yes, there are some layout algorithms that may help. A word of warning, though: your graph is very, very dense (an average of roughly 200 edges per node is a lot) which means there really is no good arrangement for your graph. Additionally, your nodes are too small to display 200 connecting edges in a nice manner. E.g. take your two left most nodes. If there are 200 edges connecting these two nodes, the nodes should be at least 400px wide - 1px for each edge (assuming an edge width of 1px) and 1px space between adjacent edges - otherwise it will not be possible to discern individual edges.
That said, the simplest solution is first increasing your node sizes and then running "Layout" -> "Hierarchic Layout".
If you need to position the nodes yourself, you can run "Layout" -> "Edge Routing" -> "Orthogonal/Polyline" or "Tools" -> "Route Parallel Edges" instead. Both of these algorithms keep the nodes are their current positions. You probably need to place your nodes further apart to ensure there is enough space for edge routes, though.
For completeness sake, I would like to mention "Layout" -> "Orthogonal" as another algorithm that will distribute edges. However, the orthogonal layout algorithm is usually not a good choice for dense graphs.