In[]:=
RandomChoice[VertexList[euc]]
Out[]=
Book10,Theorem112
In[]:=
Subgraph[euc,VertexOutComponent[euc,"Book"10,"Theorem"112,1],GraphLayout"SpringElectricalEmbedding"]
Out[]=
In[]:=
Subgraph[euc,VertexOutComponent[euc,"Book"10,"Theorem"112,2],GraphLayout"SpringElectricalEmbedding"]
Out[]=
In[]:=
Subgraph[euc,VertexOutComponent[euc,"Book"10,"Theorem"112,3],GraphLayout"SpringElectricalEmbedding"]
Out[]=
In[]:=
LayeredGraphPlot[%,"Book"10,"Theorem"112,AspectRatio1/2]
Out[]=

Color code books in main graph