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The $\Upsilon$ invariant is a concordance invariant defined by using knotFloer homology. F\"{o}ldv\'{a}ri gives a combinatorial restructure of it usinggrid homology. We extend the combinatorial $\Upsilon$ invariant for balancedspatial graph using grid homology for balanced spatial graph. Regarding linksas spatial graphs, we give a upper and lower bounds for $\Upsilon$ when twolinks are connected by a cobordism. Also we show that the combinatorial$\Upsilon$ is a concordance invariant for knots.

Concordance invariant $\Upsilon$ for balanced spatial graphs using grid homology