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All graph data structure can be serialized using the .NET serialization mechanism. You can also use the SerializeToBinary extension methods.
SerializeToBinary
varg= ...;// some graphusing(varstream=File.Open("graph.bin"))g.SerializeToBinary(stream);
AdjacencyGraph<TVertex,TEdge>g;// some graphusing(varstream=File.Open("graph.bin"))g=stream.DeseralizeFromBinary();