I don't think the general property of expander graphs is needed, perhaps a relaxed property, such as the following definition: A graph G is a distance(k)-expa

I don't think the general property of expander graphs is needed, perhaps a relaxed property, such as the following definition: A graph G is a distance(k)-expander if #edges(U, V-U) > c min(#U,#(V-U)) where U is a set of diameter <=k. Now study the embeding. I am also curious about what happens if one use SVM to classify vertices of an expander graph: Let G be an expander graph and let u1,u2 be vertices of G such that d(u1,u2) = diameter of G = an even number 2k. We classify the vertices of G like this: f(u) = 0 if d(u,u1)<=k, f(u)=1 if d(u,u1)>=1, then using SVM applied to the vertices encoded by the rows of the adjancecy matrix. I would expect the SVM algorith to have some special property but I don't know what to expect, the best or worst classification, or the support vectors can gives us some information about symmetries in the graph.