subgraph from graph matlab function

if i have a graph such as

WW = [20 10 12 14 12 10 20]; 
from=[1 2 2 3 4 3 5];
to = [4 1 4 2 3 5 4];
DG = sparse(from,to,WW); UG = tril(DG + DG');
d=graphallshortestpaths(UG,'directed',false);

is there any method to take subgraph for example(graph that contain only nodes 1 3 5)

thanks in advance

hassan

Answer 1

[ag]

Hi Hassan,

To extract a subgraph containing only specific nodes from an undirected graph, you can use the "subgraph" function in MATLAB. However, since "distance" ("graphallshortestpaths" is deprecated) returns a distance matrix rather than a graph object, you will need to first create a graph object from the adjacency matrix.

The below code snippets illustrates how to achieve this:

WW = [20 10 12 14 12 10 20];
from = [1 2 2 3 4 3 5];
to = [4 1 4 2 3 5 4];

% Create a sparse adjacency matrix for the directed graph
DG = sparse(from, to, WW)

DG = 5x5 sparse double matrix (7 nonzeros)
   (2,1)       10
   (3,2)       14
   (4,3)       12
   (1,4)       20
   (2,4)       12
   (5,4)       20
   (3,5)       10

% Convert the directed graph to an undirected graph
UG = DG + DG';

% Create a graph object from the undirected adjacency matrix
G = graph(UG);

% Compute all-pairs shortest paths (distance matrix)
d = distances(G);

% Specify the nodes for the subgraph
selectedNodes = [1, 3, 5];

% Create the subgraph containing only the specified nodes
subG = subgraph(G, selectedNodes);

% Display the subgraph
plot(subG, 'EdgeLabel', subG.Edges.Weight);

Please note, that the node numbering in the subgraph is reset.

For more details, please refer to the following MathWorks documentations:

• distances - https://www.mathworks.com/help/matlab/ref/graph.distances.html
• subgraph - https://www.mathworks.com/help/matlab/ref/graph.subgraph.html#:~:text=The%20node%20numbering%20in%20the%20subgraph%20is%20reset

Hope this helps!