Multiple short path with condition

I am trying to find shortest distance from all points to all other points in my dataset.

the data set contains network lines and points 
The points feature has only types (A,B).100+ points of typeA and 500+ points of type B.

Is it possible in FME  to have the short path finder to search the short path always starts from point A to pint B.
Then write the output to writer.