T-modulated differential scanning calorimetry measurements on bulk ${\mathrm{As}}_{x}{\mathrm{Se}}_{1\ensuremath{-}x}$ glasses show that the glass transition temperature ${T}_{g}(x)$ variation at $xl0.12$ is linear with a slope ${\mathrm{dT}}_{g}/dx=4.1\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}/\mathrm{at}.%\mathrm{As},$ and the nonreversing heat flow, $\ensuremath{\Delta}{H}_{\mathrm{nr}}(x)$ almost vanishes in the 0.291(1)x0.37(1) composition range. These thermal results analyzed by agglomeration theory and constraint theory suggest that in addition to $\mathrm{As}({\mathrm{Se}}_{1/2}{)}_{3}$ units, quasitetrahedral ${\mathrm{S}\mathrm{e}=\mathrm{A}\mathrm{s}(\mathrm{S}\mathrm{e}}_{1/2}{)}_{3}$ units also serve to crosslink ${\mathrm{Se}}_{q}$ chains at $x\frac{2}{5}.$ The results also suggest that rigidity onsets at ${r}_{c}(1)=2.29(1)$ and the transition to the stressed rigid phase occurs at ${r}_{c}(2)=2.37(1),$ below the chemical threshold at ${r}_{\mathrm{ct}}=2.40$ (or $x=\frac{2}{5}).$