QuickGraph Serialization, custom Vertices and Edges

Question

my goal is to store a BidirectionalGraph.
Due to the fact that I process big data, a xml file is not usable. Unfortunately the program has to work without a database.
Therefore I need a way to serialize the graph memory- efficiently.

I tried .NET Serialization and GraphML Serialization. But none of them worked.

Using .Net I get that error: "no implicit reference conversion..." due to the missing [Serializable] statement at BidirectionalGraph- class.
Using xmlwriters I get a System.NotSupportedException: "Property type MyEdge.Source not supported by the GraphML schema&quot"

I already marked my custom vertex class and edge class serializable.
The EdgeClass implements IEdge and has two additional int attributes.
The VertexClass has int attributes as well as a dictionary and a list.

Maybe someone can help me make BidirectionalGraph serializable or got another solution?
Thank you for your help in this matter.