Hello @soly, thanks for posting! May I ask what format the source/input data is currently in? (eg. what format reader is being used?)
Are we working with a combination of lines and points, or just lines? Also, is the data spatially aware? (eg. does it belong to a geographical area or coordinate system?). 
Further, the image shows two End Points. Should there be a path between every point and both end points? Also, do the points also have IDs? Happy to help, Kailin.

It is file geodatabase and .every point has his own id .

i have point data and also lines ,it has coordinate system .the paths is shown explained as picture .

Do you have any suggestion?

Hey @soly, you can try using a TopologyBuilder to relate the points to the line(s) that they intersect. Otherwise, could you try building paths, then using the ShortestPathFinder to identify routes from start to finish. The result of the ShortestPathFinder is an actual IFMEPath, which could be split up into the records for XLSXW.  Ideally there would be just one path between the points. There are some great examples of how to use the ShortestPathFinder in the linked article! Hope this helps, Kailin.

@kailinatsafe 

thanks for reply ,but what should I do if there are more than one path from start point to end point .

how could I get all paths ?

Hello @soly, you would likely need to create a separate path for each start feature, then calculate their own shortest paths! Kailin. 

@kailinatsafeThanks ,i will try to do it .the problem ,it means I have to use shortest path finder more than one time and I am not sure how many paths that I have .
i have read article about first depth search ,to trace the paths but I am not sure how could I use here .Do you have FME workspace template for using first depth search to understand the logic ?

Hello @soly, I have not tested this, but I might use the TopologyBuilder to identify the Start and End points of each pathway. Next, we would need to create the line/path geometry between the Start and End points, perhaps a LineBuilder could be used. Once the line is created, you can send it to the ShortestPathFinder as the ‘From-To’ input. Check out Example1.fmwt from the Shortest Path Tutorial! Consider sharing a workspace template if you are still having issues! Happy to help, Kailin.