I have a fairly sparse adjacency matrix for which I can draw the graph. Right now, two nodes $i$ and $j$ are connected, or not ($w_{ij} \in \{0,1\}$). However, I have come up with a way to define new connections between previously unconnected vertices, and assign some value $0\le w_{ij}\le 1$ to these new edges. I want the resulting graph to be drawn with these new edges taken into account as far as the layout is concerned (i.e. the spring-electrical-embedding algorithm should include these edges). I do not, however, want these edges to be drawn visually.
The only solution I can come up with myself is to calculate the node-coordinates first, then cross-reference them with the adjacency-matrix and only draw the vertices in some sort of scatterplot. This seems a little inefficient and overcomplicated though... Any shortcuts?