In[]:=
InteractiveListSelectorSW[(unorderedHypergraphPlot[#]#)&/@allUnorderedHypergraphs[{{2,3}}]]
Out[]=
{{{1,2,3},{1,2,4}}}
In[]:=
InteractiveListSelectorSW[(unorderedHypergraphPlot[#]#)&/@allUnorderedHypergraphs[{{3,3}}]]
Out[]=
{{{1,2,3},{1,2,4},{3,4,5}},{{1,2,3},{1,2,4},{1,2,5}}}
{{{1,2,3},{1,2,4},{3,4,5}},{{1,2,3},{1,2,4},{1,2,5}},{{1,2,3},{1,2,4},{1,5,6}}}
{{{1,2,3},{1,2,4},{3,4,5}},{{1,2,3},{1,2,4},{1,2,5}},{{1,2,3},{1,2,4},{1,5,6}},{{1,2,3},{1,2,4},{3,4,5}}}
unorderedHypergraphPlot/@allUnorderedHypergraphs[{{2,3}}]