Highlight a sub graph with special properties

This question is related to that one:Styling a flow graph. For a demonstration of a flowgraph I "styled" such a graph (an intermediate result in the algorithm of Ford-Fulkerson) in the following way:

    display = {Property["s" \[DirectedEdge] 4, EdgeWeight -> "0,30"],
Property["s" \[DirectedEdge] 1, EdgeWeight -> "10"],
Property[
1 \[DirectedEdge] "s", {EdgeWeight -> "30", EdgeStyle -> Red}],
Property[
2 \[DirectedEdge] 1, {EdgeWeight -> "30", EdgeStyle -> Red}],
Property[
3 \[DirectedEdge] 2, {EdgeWeight -> "10", EdgeStyle -> Red}],
Property[4 \[DirectedEdge] 5, EdgeWeight -> "0,54"],
Property[5 \[DirectedEdge] 3, EdgeWeight -> "0,50"],
Property[6 \[DirectedEdge] 4, EdgeWeight -> "0,17"],
Property[2 \[DirectedEdge] 6, EdgeWeight -> "17"],
Property[
6 \[DirectedEdge] 2, {EdgeWeight -> "20", EdgeStyle -> Red}],
Property[6 \[DirectedEdge] "t", EdgeWeight -> "12"],
Property[
"t" \[DirectedEdge] 6, {EdgeWeight -> "20", EdgeStyle -> Red}],
Property[3 \[DirectedEdge] "t", EdgeWeight -> "12"],
Property[
"t" \[DirectedEdge] 3, {EdgeWeight -> "10", EdgeStyle -> Red}]};


This yields the following graph:

Next steps to find a path from "s" to "t", via FindPath - no problem

paths = FindPath[display, "s", "t", \[Infinity], All]
(*{{"s", 4, 5, 3, "t"}, {"s", 4, 5, 3, 2, 6, "t"}}*)


But the attempt to highlight one of these paths in the graph of the intermediate result is not successful, only the vertices are highlighted and I (so far) could not manage to get the edges highlighted (eg. dashed, or different color). So this code was (and is) nut successful:

Graph[display, EdgeLabels -> Placed["EdgeWeight", Center],
VertexLabels -> Placed["Name", Center],
GraphStyle -> "SmallNetwork", GraphHighlightStyle -> "Dashed"];


Has anyone an hint for me how to mange it? Removing the properties as in the cited question would remove "my" properties.

Side question: I used "EdgeWeight" for the capacities, if I use "EdgeCapacity" these numbers are not shown when using EdgeLabels -> Placed["EdgeCapacity", Center]. I have no idea why.

Perhaps,

Using,

g = Graph[display, EdgeLabels -> Placed["EdgeWeight", Center],
VertexLabels -> Placed["Name", Center],
GraphStyle -> "SmallNetwork"]


then,

HighlightGraph[g, {Style[#, Green] & /@ paths[[1]],
Style[#, Green] & /@ DirectedEdge @@@ Partition[paths[[1]], 2, 1]}]


or to get default highlight styles:

HighlightGraph[g, DirectedEdge @@@ Partition[paths[[1]], 2, 1],
GraphHighlightStyle -> "Dashed"]


• Thank you, this solves my problem. (I still do not understand completely why my approach did not work) I tried e.g. ´HighlightGraph[display, PathGraph[{"s", 4, 5, 3, "t"}], GraphHighlightStyle -> "Dashed"]´ but only got the vertices highlighted. Oct 26 '16 at 18:39