Subgraph from selected edges

Hi, is it possible to extract a subgraph by selecting the edges, instead of nodes? If Yes, how?

From the Matlab docs, I can see it is possible by selecting the nodes, but not the edges:

H = subgraph(G,nodeIDs)
H = subgraph(G,idx)

Answer 1

[Wan Ji]

Note that all the endnodes of some given edges may be repeated, as commented by @Sim. Unique is a good way to solve such problem, to the example provided by Sim, now the code is modified as

clc; close all; clear all;
s = [1 1 1 1 2 2 2 2  2  2  2  2  2  2 15 15 15 15 15];
t = [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20];
x = [1 2 0 0 0 1 7 8 9 10 1 2 4 3 5 6 7 8 9 10];
y = [0 1 0 1 2 2 0 1 2  3 4 5 3 5 6 3 4 6 7  8];
G = graph(s,t);
G.Nodes.X = x(:); 
G.Nodes.Y = y(:);
EdgeNumber = [1 2 15] ; % the no. of egde
EndNodes = G.Edges.EndNodes(EdgeNumber,:)
H = subgraph(G, unique(EndNodes));
figure
hold on
plot(G,'XData',x,'YData',y,'EdgeColor','blue','LineWidth',1)
h = plot(H,'XData',H.Nodes.X,'YData',H.Nodes.Y,'EdgeColor','red','LineWidth',2);
h.NodeLabel = {};

It is found that this method includes one edge more, i.e. the edge (2,15) in G. This is OK, because what the method provide is the subgraph connected with these 5 nodes.

IF YOU WANT TO get subgraph really by edges. Then

s = [1 1 1 1 2 2 2 2  2  2  2  2  2  2 15 15 15 15 15];
t = [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20];
x = [1 2 0 0 0 1 7 8 9 10 1 2 4 3 5 6 7 8 9 10];
y = [0 1 0 1 2 2 0 1 2  3 4 5 3 5 6 3 4 6 7  8];
G = graph(s,t);
G.Nodes.X = x(:); 
G.Nodes.Y = y(:);
EdgeNumber = [1 2 15] ; % the no. of egde
EndNodes = G.Edges.EndNodes(EdgeNumber,:);
[q, ~, ic]= unique(EndNodes);
p = 1:1:numel(q);
st = p(reshape(ic,size(EndNodes)));
sub_Graph_by_Egde = graph(st(:,1), st(:,2));
sub_Graph_by_Egde.Nodes.X = G.Nodes.X(q,:);
sub_Graph_by_Egde.Nodes.Y = G.Nodes.Y(q,:);
figure
hold on
plot(G,'XData',x,'YData',y,'EdgeColor','blue','LineWidth',1)
h = plot(sub_Graph_by_Egde,'XData',sub_Graph_by_Egde.Nodes.X,...
    'YData',sub_Graph_by_Egde.Nodes.Y,'EdgeColor','red','LineWidth',2);

I think I have solved your problem

[Sim]

Cool, many thanks @Wan Ji !

However, this works only with 1 edge:

clc; close all; clear all;
s = [1 1 1 1 2 2 2 2  2  2  2  2  2  2 15 15 15 15 15];
t = [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20];
x = [1 2 0 0 0 1 7 8 9 10 1 2 4 3 5 6 7 8 9 10];
y = [0 1 0 1 2 2 0 1 2  3 4 5 3 5 6 3 4 6 7  8];
G = graph(s,t);
G.Nodes.X = x(:); G.Nodes.Y = y(:);

EdgeNumber = [10] ; % the no. of egde
EndNodes = G.Edges.EndNodes(EdgeNumber,:)
H = subgraph(G, EndNodes);

figure
hold on
plot(G,'XData',x,'YData',y,'EdgeColor','blue','LineWidth',1)
h = plot(H,'XData',H.Nodes.X,'YData',H.Nodes.Y,'EdgeColor','red','LineWidth',2);
h.NodeLabel = {};

Which gives me this result:

EndNodes =
     2    11

How to make it work for many EdgeNumber ?

[Sim]

Fantastic @Wan Ji, you totally nailed it! Very grateful!

Issue solved! :-)

[Jothimani V]

hello sir

how to split subgraphs(by selected edges) from given complete graph in matlab sir?

Answer 2

[Wan Ji]

hi, friend, you can make EdgeNumber an array that contains all the edge numbers that you are interested in. and make the line H = subgraph(G, EndNodes); changed as H = subgraph(G, EndNodes(:));

[Sim]

Hi, thanks for the nice reply... I used

H = subgraph(G, unique(EndNodes));

instead of your suggestion:

H = subgraph(G, EndNodes(:));

since, with your hint, it gave me the following error:

Error using graph/subgraph (line 40)
Nodes must be a vector of unique node indices, a vector of unique node names, or a logical vector of length equal to the number of
nodes.

Now it works, but there is still an important issue to fix.

In this example:

clc; close all; clear all;
s = [1 1 1 1 2 2 2 2  2  2  2  2  2  2 15 15 15 15 15];
t = [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20];
x = [1 2 0 0 0 1 7 8 9 10 1 2 4 3 5 6 7 8 9 10];
y = [0 1 0 1 2 2 0 1 2  3 4 5 3 5 6 3 4 6 7  8];
G = graph(s,t);
G.Nodes.X = x(:); G.Nodes.Y = y(:);
EdgeNumber = [1 2 15] ; % the no. of egde
EndNodes = G.Edges.EndNodes(EdgeNumber,:)
H = subgraph(G, unique(EndNodes));
figure
hold on
plot(G,'XData',x,'YData',y,'EdgeColor','blue','LineWidth',1)
h = plot(H,'XData',H.Nodes.X,'YData',H.Nodes.Y,'EdgeColor','red','LineWidth',2);
h.NodeLabel = {};

the result is:

EndNodes =

     1     2
     1     3
    15    16

However, in the subgraph H I have an additional edge, i.e 4 edges, instead of 3 edges:

    >> H.Edges

ans =

     1    2 
     1    3 
     2    4 
     4    5 

which can be seen in the following picture too (here, the nodes labels refer to G and not to H):

This is due to the fact that I had to take the unique nodes in G, as required by the subgraph function:

     H = subgraph(G,nodeIDs)

i.e.

>> unique(EndNodes)

ans =

     1
     2
     3
    15
    16

In summary, this method includes one edge more, i.e. the edge (2,15) in G:

    EndNodes =

     1     2
     1     3
     2    15
    15    16

If we can solve this issue it is done!

[Wan Ji]

yes, you have done a good job, 👍👍👍

[Sim]

many thanks @Wan Ji! :)