  Given any (not necessarily connected) combinatorial finite graph and any
compact smooth $6$-manifold $M^6$ with the third Betti number $b_3\not=0$, we
construct a calibrated 3-dimensional homologically area minimizing surface on
$M$ equipped in a smooth metric $g$, so that the singular set of the surface is
precisely an embedding of this finite graph. Moreover, the calibration form
near the singular set is a smoothly $GL(6,\mathbb{R})$ twisted special
Lagrangian form. The constructions are based on some unpublished ideas of
Professor Camillo De Lellis and Professor Robert Bryant.
