Use a Chopper (2 vertices) and a Linecombiner.

Next use a PointOnLineOverlayer to add the ID's of the start and end vertex to the lines (generate a list containing the vertex ID's on output 'Line', and turn the list values into attributes).

Thanks for ur idea .

Could u please upload the Fme workspace to understand it better .

i am still confused about sth , the point that I will use as input for point on line ,

it should be the point that I want to find on line but how to reorder theses points .

because I think ,it brings me the output but not reordered it .

i have got the path from start node to end node (from beginning of line to end of line )

important for me to find the intermediate points and reorder them at the same direction .

I have used start node and end node as input from to line but I did not use any intermediate points but I got the paths that I want .

But it is still not clear for me ,how will reorder the intermediate point .

if says

A start node

intermediate points :

g to k

k to f

f to c

f to c

all of them has same id when it locates at same path

till reach to end of the path

end node : c to h

if u have sammele workspace ,could u upload it .

Thanks for help