Dear Biswajit,
it doesn't hurt opening a question with a friendly sentence.
Anyway, as the output tells you, your graph vertices are labelled by
strings (namely "x0", "x1", ...) which you cannot multiply as the
product of two strings is not defined here.
If you want to use variables instead, you do for example
sage: P.<x0,x1,x2,y1,y2> = PolynomialRing(QQ,5)
sage: dia = DiGraph({x0:{x1:(1, -1),y1:(1, -1),x2:(1, -1)},y2:{x0:(1,
-1),x1:(1, -1)}})
sage: diaout = dia.neighbors_out(x0);diaout
[y1, x2, x1]
sage: prod(diaout)
x1*x2*y1
Cheers, Christian
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