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3d mesh to graph conversion problem

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I have a 3D triangle mesh which is represented as an undirected graph.The nodes of the graph correspond to the vertices of the triangle and the edges to the sides.Now I need to convert this graph into a connected graph. I did a simple triangle-triangle intersection test by checking the distance of the vertices of triangle A from the plane of triangle B and if the distance is small and the point lies in the bounding box of triangle B, I add new edges from the vertices of B to the point,with the lengths of the edges corresponding to the geometrical distance. I know its not completely correct but it seems to be working fine for the meshes I tested.Does anyone know an algorithm that covers other cases too?please let me know. thanks in advance.

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