Sibshat,
The a developer you will have to create a custom widget that allows the user to add junction or edge flags and or barriers (likely using the DrawBox dijit) and then present the html select element for them to choose the parameter options like "FindPath" "Find Connected", etc and the from those inputs build your url request using the esriRequest so that it looks something like this example:
http:// sit2.sistemigis.it/sit/rest/services/Demo/GeometricNetworkStream/MapServer/exts/GeometricNetworkUtility/GeometricNetworks/1/TraceNetwork?f=json&outFields=OBJECTID&maxTracedFeatures=10000&tolerance=10&flowElements=esriFEJunctionsAndEdges&edgeFlags=[{"x":421709.64645703085,"y":5085891.334625113,"spatialReference":{"wkid":32632}},{"x":420453.2768722459,"y":5085753.698631274,"spatialReference":{"wkid":32632}}]&traceIndeterminateFlow=false&traceSolverType=FindPath&flowMethod=esriFMConnected&shortestPathObjFn=esriSPObjFnMinMax&fromToEdgeWeight=Length&toFromEdgeWeight=Length
Then finally you will have to do something with the response like add the graphics to the map.
{"segmentCosts":[2952.5300148907204],"edges":[{"displayFieldName":"","fieldAliases":{"OBJECTID":"OBJECTID"},"geometryType":"esriGeometryPolyline","spatialReference":{"wkid":32632,"latestWkid":32632},"fields":[{"name":"OBJECTID","type":"esriFieldTypeOID","alias":"OBJECTID"}],"features":[{"attributes":{"OBJECTID":584},"geometry":{"paths":[[[420494.31799999997,5086500.0399999991],[420374.31799999997,5086540.0399999991]]]}},{"attributes":{"OBJECTID":585},"geometry":{"paths":[[[420294.31799999997,5086460.0399999991],[420374.31799999997,5086540.0399999991]]]}},{"attributes":{"OBJECTID":593},"geometry":{"paths":[[[420814.31799999997,5086300.0399999991],[420654.31799999997,5086460.0399999991],[420494.31799999997,5086500.0399999991]]]}},{"attributes":{"OBJECTID":596},"geometry":{"paths":[[[421054.31799999997,5086180.0399999991],[420974.31799999997,5086260.0399999991],[420814.31799999997,5086300.0399999991]]]}},{"attributes":{"OBJECTID":597},"geometry":{"paths":[[[421094.31799999997,5086140.0399999991],[421054.31799999997,5086180.0399999991]]]}},{"attributes":{"OBJECTID":607},"geometry":{"paths":[[[421794.31799999997,5085900.0399999991],[421334.31799999997,5085900.0399999991],[421094.31799999997,5086140.0399999991]]]}},{"attributes":{"OBJECTID":617},"geometry":{"paths":[[[420714.31799999997,5085480.0399999991],[420494.31799999997,5085660.0399999991],[420414.31799999997,5085860.0399999991],[420254.31799999997,5086020.0399999991],[420214.31799999997,5086300.0399999991],[420294.31799999997,5086460.0399999991]]]}}]}],"junctions":[{"displayFieldName":"","fieldAliases":{"OBJECTID":"OBJECTID"},"geometryType":"esriGeometryPoint","spatialReference":{"wkid":32632,"latestWkid":32632},"fields":[{"name":"OBJECTID","type":"esriFieldTypeOID","alias":"OBJECTID"}],"features":[{"attributes":{"OBJECTID":248},"geometry":{"x":420294.31799999997,"y":5086460.0399999991}},{"attributes":{"OBJECTID":252},"geometry":{"x":420374.31799999997,"y":5086540.0399999991}},{"attributes":{"OBJECTID":256},"geometry":{"x":420494.31799999997,"y":5086500.0399999991}},{"attributes":{"OBJECTID":272},"geometry":{"x":420814.31799999997,"y":5086300.0399999991}},{"attributes":{"OBJECTID":290},"geometry":{"x":421054.31799999997,"y":5086180.0399999991}},{"attributes":{"OBJECTID":293},"geometry":{"x":421094.31799999997,"y":5086140.0399999991}}]}],"flagsNotFound":[],"barriersNotFound":[]}
This not something that someone is going to be able to just send you a couple of lines of code for. Developing this widget would involve a fair level of effort. If you are not a developer I would suggest you contact esri professional services or hire a GIS consulting company.
