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The command ShowGraph[] converts a Graph object in a Graphics object containing points and lines as a set of separate graphics primitives.

The adjacency matrix is stored in full size in the Graph object.

JavaView receives a graph as two separate geometries, a point set and a polygon set. The point set is obsolete if the the vertices of the polygon set are made visible.

In[1]:= <<DiscreteMath`Combinatorica`
In[2]:= sg = ShowGraph[GridGraph[3, 3]]

In[3]:= JavaView[sg]

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