There is a simple way to do this that should be very easy to implement. Split the graph into the nodes 1 - 50 and the nodes 51 - 100. Then, lay out these groups of nodes, independently, into two rings, and connect each node in the first group to the three nodes that immediately follow it and each node in the second group to the ten nodes that immediately follow it. That gives you the properties you want.
Hope this helps!