, edge_connectivity . source target, :
 sapply(V(g) , function(v) if( v != 5){edge_connectivity(g, source=v, target=5)} else NA )
 a  b  c  d  e  f  g  h  i  j  k  l  m  n  o  p  q  r  s  t 
 1  0  0  0 NA  0  0  0  0  0  0  0  0  1  0  0  0  1  0  1 
 
 
 V(g)[ which(e_con >0)]
+ 4/20 vertices, named, from ba45ff0:
[1] a n r t
:
small_g <- delete_vertices( g, !V(g) %in% c(5, V(g)[ which(econ >0)] ))
plot( small_g)

:
edges(small_g)
[[1]]
IGRAPH 11d63f6 DN-- 5 4 -- Erdos renyi (gnp) graph
+ attr: name (g/c), type (g/c), loops (g/l), p (g/n), name (v/c)
+ edges from 11d63f6 (vertex names):
[1] n->a t->a a->e r->e