error in finding shortest path

I have created a graph with values

y =

   (1,3)       0.8615
   (2,3)       0.8479
   (1,5)       0.1064
   (2,5)       0.9705
   (3,5)       0.6588
   (4,5)       0.8535
   (1,6)       0.3939
   (3,6)       0.7948
   (1,7)       0.5726
   (4,7)       0.6146
   (6,7)       0.8340
   (2,8)       0.6760
   (4,8)       0.5518
   (5,8)       0.7033
   (4,9)       0.2783
   (7,9)       0.3425
   (8,9)       0.7412

bg=(biograph(y,[],'ShowArrows', 'off','ShowWeights','on'));

view(bg)

now i have found shortest path between two nodes,it works for some nodes and gives the path and distance,but for some nodes the path is empty ,for example

[dist,path,pred] = graphshortestpath(y,3,4)

the path is empty, kindly tell why i get empty path

Answer 1

[Walter Roberson]

Links are unidirectional.

You have a link from 3 to 5 and from 3 to 6.

If you use (3,5) then the only link from 5 is (5,8) so you have to take that. Once you are at 8, the only link is (8,9) so you take that. There are no links from 9 so the path is a dead end.

So you need to instead use (3,6). Once you are at 6 the only link is (6,7) so you have to take that. Once you are at 7, the only link is (7,9) so you take that. There are no links from 9 so the path is a dead end.

Therefor with the data matrix you have, there is no route from 3 to 5.

If you want the routes to be symmetric then you need to add in the symmetric entries.

Y = y + y';

Now if you ask for the path on Y you will get a result.