How can I find if edges in a subgraph SG appear inside/belong to a graph G?

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How can I find if edges in a subgraph SG appear inside/belong to a graph G?
I have this example with a graph G:
s = [1 1 2 2 2 3 3 3];
t = [2 3 3 4 5 6 7 5];
x = [0 0 1 0 4 3 1];
y = [0 1 0 4 5 0 -1];
G = graph(s,t);
G.Nodes.X = x'; G.Nodes.Y = y';
plot(G,'XData',G.Nodes.X,'YData',G.Nodes.Y)
From the graph G I "extract" a subgraph SG, i.e.:
SG = subgraph(G,[2 3 5 6])
figure
plot(SG,'XData',SG.Nodes.X,'YData',SG.Nodes.Y)
Now I would like to find the edges of SG inside/which belong to G. The answer should be:
edges_in_G =
2 3
2 5
3 5
3 6
% which correspond to
edges_in_SG =
1 2
1 3
2 3
2 4
How to do it since the nodes in the subgraph SG are renumbered (compared to the graph G)?
  4 Comments
Jon
Jon on 26 Jan 2022
Hi I'm glad that approach worked for you. Good idea for the automatic generation of unique edge names. Thanks for putting all of the pieces together so the answer is clearer. Good luck with your project.

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Accepted Answer

Jon
Jon on 25 Jan 2022
You can name the edges in G and then the corresponding edges in the subgraph will have the same names as those in the main graph. So something like this:
s = [1 1 2 2 2 3 3 3];
t = [2 3 3 4 5 6 7 5];
x = [0 0 1 0 4 3 1];
y = [0 1 0 4 5 0 -1];
G = graph(s,t);
G.Nodes.X = x'; G.Nodes.Y = y';
% Name the edges, column name in edge table must be "Names"
G.Edges.Names = {'a','b','c','d','e','f','g','h'}'
plot(G,'XData',G.Nodes.X,'YData',G.Nodes.Y)
% From the graph G I "extract" a subgraph SG, i.e.:
SG = subgraph(G,[2 3 5 6])
figure
plot(SG,'XData',SG.Nodes.X,'YData',SG.Nodes.Y)
% find out which edges in SG are in G
idl = ismember(G.Edges.Names,SG.Edges.Names)
inG = G.Edges.Names(idl)
  3 Comments
Jon
Jon on 25 Jan 2022
Edited: Jon on 25 Jan 2022
Oh, I just saw that you want the edges in G listed by their end nodes, you can do this, using the logical index idl from above and
idl = ismember(G.Edges.Names,SG.Edges.Names)
edges_in_G = G.Edges.EndNodes(idl,:)
edges_in_G =
2 3
2 5
3 5
3 6
Sim
Sim on 26 Jan 2022
Edited: Sim on 26 Jan 2022
thanks a lot @Jon!
the only thing is that I have a graph of around 5000 edges and 9000 nodes..... probably I need to use a name/label with numbers instead of letters, or a combination of numbers and letters?... thanks :)
EDITED: I found a simple (and "automatic") way to name all the edges:
G.Edges.Names = compose('edge_%d',1 : numedges(G))';
In case other people are interested, I just rewrite here your entire solution, since it was fragmented in different comments:
% code from @Jon (with a very tiny modification)
close all; clc;
s = [1 1 2 2 2 3 3 3];
t = [2 3 3 4 5 6 7 5];
x = [0 0 1 0 4 3 1];
y = [0 1 0 4 5 0 -1];
% create the graph G
G = graph(s,t);
G.Nodes.X = x'; G.Nodes.Y = y';
% name the edges, column name in edge table must be "Names"
G.Edges.Names = compose('edge_%d',1 : numedges(G))';
% extract a subgraph SG from the graph G
SG = subgraph(G,[2 3 5 6]);
% plot G and SG
figure
h = plot(G,'XData',G.Nodes.X,'YData',G.Nodes.Y);
labeledge(h,1:numel(G.Edges.Names),G.Edges.Names)
figure
h = plot(SG,'XData',SG.Nodes.X,'YData',SG.Nodes.Y);
labeledge(h,1:numel(SG.Edges.Names),SG.Edges.Names)
% show edges of SG and find out which edges in SG are in G
edges_in_SG = SG.Edges.EndNodes
idl = ismember(G.Edges.Names,SG.Edges.Names);
inG = G.Edges.Names(idl)
edges_in_G = G.Edges.EndNodes(idl,:)
% results from @Jon
edges_in_SG =
1 2
1 3
2 3
2 4
inG =
4×1 cell array
{'edge_3'}
{'edge_5'}
{'edge_6'}
{'edge_7'}
edges_in_G =
2 3
2 5
3 5
3 6

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