All graph data structure can be serialized using the .NET serialization mechanism. You can also use the SerializeToBinary extension methods.

Writing

var g = ...; // some graph
using(var stream = File.Open("graph.bin"))
    g.SerializeToBinary(stream);

Reading

AdjacencyGraph<TVertex,TEdge> g; // some graph
using(var stream = File.Open("graph.bin"))
    g = stream.DeseralizeFromBinary();