How does shortestpath function work?

Hi everyone. i need a help.

i don't completely understand the "Shortest Path in Multigraph" example in "shortestpath" function (in particular, the edgepth). i don't understand the meaning of the indeces [1 7 9 10]: i thought they were the indeces of the couples of coordinates, but -if i were right- these couples shoud be 1-2/2,4/3,5/3,5 (that are not the right ones, couse in the "highlight" part and in the plot part everithing is ok.

Thx for your help

Answer 1

[Christine Tobler]

Every edge has a number, which is the order in which they appear in the Edges table (try displaying g.Edges). The edgepath contains the number of each edge on the path:

G = graph([1 1 1 1 1 2 2 3 3 3 4 4],[2 2 2 2 2 3 4 4 5 5 5 2],[2 4 6 8 10 5 3 1 5 6 8 9])

G = 
  graph with properties:

    Edges: [12×2 table]
    Nodes: [5×0 table]

G.Edges

ans = 12×2 table
    EndNodes    Weight
    ________    ______

     1    2        2  
     1    2        4  
     1    2        6  
     1    2        8  
     1    2       10  
     2    3        5  
     2    4        3  
     2    4        9  
     3    4        1  
     3    5        5  
     3    5        6  
     4    5        8  

So the array [1 7 9 10] points to the first, 7th, 9th and 10th rows of the Edges table as the edges on the path (this is relevant for a multigraph because there can be several edges between the same two nodes).

If we index into the Edges table using edgepath, we get just a table of the edges that are on the path (see g.Edges(edgepath, :) in the example).

[Riccardo Nebuloni]

thank you @Christine Tobler, now i get it.

as you can see the indeces of the input "lines" are different to the ones found in the table. is there a way to keep the same order of the input data?

[Christine Tobler]

Do you mean the values in the Weight column of the Edges table? Those are just inserted as being the "length" of each edge, they're not supposed to map to the edge indices.

[Riccardo Nebuloni]

no, i mean the first two vectors inside []:

lets call them a=[1 1 1 1 1 2 2 3 3 3 4 4] and b= [2 2 2 2 2 3 4 4 5 5 5 2].

the branch matrix will be C= [a' b']. i will obtain line indeces that link the starting and final points of a branch eg:

1. 1-2
2. 1-2
3. 1-2
4. 1-2
5. 1-2
6. 2-3
7. 2-4
8. 3-4
9. 3-5
10. 3-5
11. 4-5
12. 4-2

this order is not the same of the first two columns of the table. my question is: is there a way to keep the input order of the nodes?

[Christine Tobler]

I see. The Edges table is always put into a standard format, as this makes it easier to compare graphs and the algorithms are much more efficient this way.

You can maintain the information about the original order of the edges by having the weights of the graph store this original order:

a=[1 1 1 1 1 2 2 3 3 3 4 4];
b= [2 2 2 2 2 3 4 4 5 5 5 2];
G = graph(a, b, 1:length(a));
G.Edges

ans = 12×2 table
    EndNodes    Weight
    ________    ______

     1    2        1  
     1    2        2  
     1    2        3  
     1    2        4  
     1    2        5  
     2    3        6  
     2    4        7  
     2    4       12  
     3    4        8  
     3    5        9  
     3    5       10  
     4    5       11  

Here the weight of each edge is giving the order in which it appeared in the original inputs.