Get shortest paths and distances among nodes without loop for (and possibly in a faster way)

How to get shortest paths and distances among nodes (selected from a list) without a loop for, and possibly in a faster way than what shown in the following example ?

% Input 1 (the graph)
s = [1 1 1 1 2 2 2 2 2 8 8 12 14 14 1 14];
t = [3 5 4 2 6 10 7 9 8 11 12 13 7 6 8 15];
G = graph(s,t);
plot(G)

% Input 2 (list of nodes, among which, both shortest paths and distances will be
% calculated)
list = [3 7 8 9 10 14];

% Calculation
tic
for i = 1 :length(list)
    for j = 1 : length(list)
        [p,d] = shortestpath(G,list(i),list(j));
        nodes_path{i,j} = p;
        nodes_distances{i,j} = d;
    end
end
toc

Elapsed time is 0.016856 seconds.

% Outputs
nodes_path,

nodes_path = 6×6 cell array
    {[         3]}    {[3 1 2 7]}    {[   3 1 8]}    {[ 3 1 2 9]}    {[ 3 1 2 10]}    {[3 1 2 6 14]}
    {[   7 2 1 3]}    {[      7]}    {[   7 2 8]}    {[   7 2 9]}    {[   7 2 10]}    {[      7 14]}
    {[     8 1 3]}    {[  8 2 7]}    {[       8]}    {[   8 2 9]}    {[   8 2 10]}    {[  8 2 6 14]}
    {[   9 2 1 3]}    {[  9 2 7]}    {[   9 2 8]}    {[       9]}    {[   9 2 10]}    {[  9 2 6 14]}
    {[  10 2 1 3]}    {[ 10 2 7]}    {[  10 2 8]}    {[  10 2 9]}    {[       10]}    {[ 10 2 6 14]}
    {[14 6 2 1 3]}    {[   14 7]}    {[14 6 2 8]}    {[14 6 2 9]}    {[14 6 2 10]}    {[        14]}

nodes_distances,

nodes_distances = 6×6 cell array
    {[0]}    {[3]}    {[2]}    {[3]}    {[3]}    {[4]}
    {[3]}    {[0]}    {[2]}    {[2]}    {[2]}    {[1]}
    {[2]}    {[2]}    {[0]}    {[2]}    {[2]}    {[3]}
    {[3]}    {[2]}    {[2]}    {[0]}    {[2]}    {[3]}
    {[3]}    {[2]}    {[2]}    {[2]}    {[0]}    {[3]}
    {[4]}    {[1]}    {[3]}    {[3]}    {[3]}    {[0]}

[Matt J]

If there were a way, I think shortestpath() itself would already offer vectorized input/output, using that method.

[Sim]

Thanks @Matt J, Yes, I was thinking the same... :-)

Answer 1

[Jon]

for the distances (shortest path) between every pair of nodes in the graph

d = distances(G)

and for some subset, in your case list

d = distances(G,list,list)

[Sim]

thanks @Jon about the distances!

But what about the shortest paths?

P.S.: I would like to have both quantities (i.e. shortest paths and distances) before accepting any reply :-)

[Jon]

The distances are, by definition, the shortest paths

[Jon]

So are you clear on this now, or would you like a further explanation