Grid drawings of graphs with constant edge-vertex resolution

We study the algorithmic problem of computing drawings of graphs in which (i) each vertex is a disk with fixed radius ρ, (ii) each edge is a straight-line segment connecting the centers of the two disks representing its end-vertices, (iii) no two disks intersect, and (iv) the distance between an edge segment and the center of a non-incident disk, called edge-vertex resolution, is at least ρ. We call such drawings disk-link drawings.