<< DiscreteMath`Combinatorica`
gg = 
        FromOrderedPairs[ToUnorderedPairs[CompleteGraph[3]]];
A = 
        Transpose[
          IncidenceMatrix[ReverseEdges[gg]] - 
            IncidenceMatrix[gg]];
L = Transpose[A] . A;
u = {a, b, c};
f = -L . u + l u + u^3;
pl = {};
For[ll = 3, ll > -4, 
      ll = ll -  .01, 
ff = 
        f /. l -> ll; 
ssr = 
        Solve[ff == 0 u, 
          VerifySolutions -> True]; 
ss = {a, b, c} /. 
          ssr; 
ss = ss // N; 
s = 
        Select[ss, Element[#, Reals] &]; 
no = 
        Union[Map[Abs[#[[1]]]  &, s]]; 
pl = 
        Union[pl, 
          Map[{ll, #}  &, 
            no]];
]

ListPlot[pl, PlotStyle -> PointSize[0.002]]