Trace the path of line and extract the id for each line then repeat from start point and start again to the next path in the map....

If it were me, I would run the network through a TopologyBuilder and then use a PythonCaller to run a DepthFirstSearch.

honestly,i was trying to do it by looping but i did not success but i will try ur suggestion but about shortestpathfinder ,i was thinking about it but the problem i want to do it by unknown lines with different id not i define for each line which point will be the start and the end . thanks for reply

I don't have a script for exactly what you want to do.   A DFS  requires the data to be in a graph.  The following code sets up a weighted graph  and has a method for DFS,  but you would have to adapt the close method of the FeatureProcessor to output what you want.  

Note that the edge port of the topologyBuider should be connected to the python caller.

Also note that you probably don't care about edge weights and can simplify the code to remove them.

import fme
import fmeobjects

# Graph class structure adapted from http://www.bogotobogo.com/python/python_graph_data_structures.php
class Vertex:
    def __init__(self, node):
        self.id = node
        self.adjacent = {}

    def __str__(self):
        return str(self.id) + ':'+str([x.id for x in self.adjacent])

    def add_neighbor(self, neighbor, weight=0, edgeID=0):
        self.adjacent[neighbor.id] = (edgeID,weight)

    def get_connections(self):
        return self.adjacent.keys()  

    def get_id(self):
        return self.id

    def get_weight(self, neighbor):
        return self.adjacent[neighbor][1]
    
    def get_edgeID(self, neighbor):
        return self.adjacent[neighbor][0]

class Graph:
    def __init__(self):
        self.vert_dict = {}
        self.num_vertices = 0

    def __iter__(self):
        return iter(self.vert_dict.values())

    def add_vertex(self, node):
        self.num_vertices = self.num_vertices + 1
        new_vertex = Vertex(node)
        self.vert_dict[node] = new_vertex
        return new_vertex

    def get_vertex(self, n):
        if n in self.vert_dict:
            return self.vert_dict[n]
        else:
            return None

    def add_edge(self, frm, to, cost = 0, edgeID=0):
        if frm not in self.vert_dict:
            self.add_vertex(frm)
        if to not in self.vert_dict:
            self.add_vertex(to)

        self.vert_dict[frm].add_neighbor(self.vert_dict[to], cost, edgeID)
        self.vert_dict[to].add_neighbor(self.vert_dict[frm], cost, edgeID)

    def get_vertices(self):
        return self.vert_dict.keys()


def DFS(G,v,seen=None,path=None, cost=None):
    if seen is None: seen = []
    if path is None:
        path = []

    if cost is None:
        cost = 0

    seen.append(v)

    paths = []
    w = G.get_vertex(v)
    
    for s in w.get_connections():
        c = w.get_weight(s)    
        eID = w.get_edgeID(s)
        if s not in seen:
            s_path = path + [eID]
            s_cost = cost + c
            paths.append(((s_path), s_cost, s))
            paths.extend(DFS(G, s, seen, s_path, s_cost))
    return paths

class FeatureProcessor(object):
    def __init__(self):
        self.graph = Graph()
        self.featureList =[]

    def input(self,feature):

        #get the nodes and id of the edge
        arcID = feature.getAttribute('_edge_id')
        fN = feature.getAttribute('_from_node')
        tN = feature.getAttribute('_to_node')
        
        #calculate the length of the edge
        length = feature.getGeometry().getLength(False)
        #add them to the graph
        self.graph.add_edge(fN,tN,length, arcID)
        #add feature to featureList
        self.featureList.append(feature)
         
    def close(self):
        sV = self.graph.get_vertices()[0]
        paths = DFS(self.graph, sV)

import fme
import fmeobjects

# Graph class structure adapted from http://www.bogotobogo.com/python/python_graph_data_structures.php
class Vertex:
    def __init__(self, node):
        self.id = node
        self.adjacent = {}

    def __str__(self):
        return str(self.id) + ':'+str([x.id for x in self.adjacent])

    def add_neighbor(self, neighbor, weight=0, edgeID=0):
        self.adjacent[neighbor.id] = (edgeID,weight)

    def get_connections(self):
        return self.adjacent.keys()  

    def get_id(self):
        return self.id

    def get_weight(self, neighbor):
        return self.adjacent[neighbor][1]
    
    def get_edgeID(self, neighbor):
        return self.adjacent[neighbor][0]

class Graph:
    def __init__(self):
        self.vert_dict = {}
        self.num_vertices = 0

    def __iter__(self):
        return iter(self.vert_dict.values())

    def add_vertex(self, node):
        self.num_vertices = self.num_vertices + 1
        new_vertex = Vertex(node)
        self.vert_dict[node] = new_vertex
        return new_vertex

    def get_vertex(self, n):
        if n in self.vert_dict:
            return self.vert_dict[n]
        else:
            return None

    def add_edge(self, frm, to, cost = 0, edgeID=0):
        if frm not in self.vert_dict:
            self.add_vertex(frm)
        if to not in self.vert_dict:
            self.add_vertex(to)

        self.vert_dict[frm].add_neighbor(self.vert_dict[to], cost, edgeID)
        self.vert_dict[to].add_neighbor(self.vert_dict[frm], cost, edgeID)

    def get_vertices(self):
        return self.vert_dict.keys()


def DFS(G,v,seen=None,path=None, cost=None):
    if seen is None: seen = []
    if path is None:
        path = []

    if cost is None:
        cost = 0

    seen.append(v)

    paths = []
    w = G.get_vertex(v)
    
    for s in w.get_connections():
        c = w.get_weight(s)    
        eID = w.get_edgeID(s)
        if s not in seen:
            s_path = path + [eID]
            s_cost = cost + c
            paths.append(((s_path), s_cost, s))
            paths.extend(DFS(G, s, seen, s_path, s_cost))
    return paths

class FeatureProcessor(object):
    def __init__(self):
        self.graph = Graph()
        self.featureList =[]

    def input(self,feature):

        #get the nodes and id of the edge
        arcID = feature.getAttribute('_edge_id')
        fN = feature.getAttribute('_from_node')
        tN = feature.getAttribute('_to_node')
        
        #calculate the length of the edge
        length = feature.getGeometry().getLength(False)
        #add them to the graph
        self.graph.add_edge(fN,tN,length, arcID)
        #add feature to featureList
        self.featureList.append(feature)
         
    def close(self):
        sV = self.graph.get_vertices()[0]
        paths = DFS(self.graph, sV)

it will be nice,if u have example for this script pf python caller in fme ,i want to see how it looks like the result inside FME

where should  i write my start node .Thanks for helping

Similarly, for a recent project the solution was ShortestPathFinder for an identical problem.

This performs network/graph tracing quite effectively:

• Remove all the non-intersection intermediate line vertices with VertexRemover as don't want their vertex coordinates in the final path result.
• Create an unconstrained join between all Start and End Nodes to return groups of StartNodeID and EndNodeID
• Create To-From Lines with these Point pairs and feed these into ShortestPathFinder, which will return Path Features. Path features are a collection of all the individual path segment features and their vertices
• Rationalise these to single polylines using GeometryRefiner which will orient all the path segments in the correct direction.
• Return all the path vertices from Start to End Point with CoordinateExtractor. This will return all path point coordinates in order from start to end of the path.

could i ask ,

Create an unconstrained join between all Start and End Nodes to return groups of StartNodeID and EndNodeID

please,could you explain more ,i did not get this step

and also what u mean in this step Create To-From Lines with these Point pairs .

which transformers are doing theses steps

i need at the end each line id and if did vertex remover so the lines are intersected will be one line and may be get new id but i need the original id or each line,is it possible

Thanks alot for helping

sry for that i like ur idea but iam using fme 2018 so iam not able to open it .could u provide me with version 2018.Thanks alot

Sorry for the delayed response. Please see attached workspace recreated in 2018 version. PathFinder_2018.fmwI noticed the LineBuilder in this version (Build 18283) didn't have GroupBy function, so I added a FeatureHolder and a Sorter so that the From/To Lines were created with correct pairs of start/end nodes (i.e. start and end nodes have the same _count number).

could i ask if i have area between lines ,which transformers suggested u to continue following the path .Thanks alot for upload another version

Could you give a bit more details (or an example if that's easier) on your case? By having area between lines, does that mean the input data has mixed geometry of polygons and line segments? If so, the Chopper could still work to break down the polygon into its exterior lines (Mode: By Vertex, Maximum Vertices: 2).