Give a graph G enumerate all possible shortest paths from that vertex to all other vertices like

From vertex v1

P1={(1,2),(2,3)} shortest path from 1 to 3 is stored in P1

P2={(1,2)} shortest path from 1 to 2 of length 1 

Put all possible path of length k  from a verex v in a list seperate

That is length 1 in a seperate from vertex v in a seperate list 

Etc

Function with be F(Graph::G,v)

Function will return all those lists

restart;
with(GraphTheory);
with(combinat, cartprod);
with(SpecialGraphs);
with(RandomGraphs);

Given any arbitary graph G how many possible paths of length k are possible

G := CartesianProduct(PathGraph(3), PathGraph(3));
s := AllPairsDistance(FLT)

How to find how may possible paths of length say 4 from vertex 1:1 

" for example this CartesianProduct(Path(3),Path(3)) number of possible paths of length 2 are

1:1 - 1:2 -2:2

1:1 -2:1-2:2

1:1-1:2 -1:3

1:1-2:1-3:1

so a total of 2 length paths 

next say how may possible paths of length say 3 from vertex 1:2

similar given a vertex and path length how many possible path of that length are possible from that vertex.

It is not restricted to this graph given any graph G in general , a vertex v and k a path length i should get total number of paths of that length in that graph G

That is function say   F(G::Graph,vertex,k) i should get output of the number of path of length k from that vertex v. 

"Only a idea but I may be wrong 

I had an idea taking a row of a vertex in the graph G in the shortest path matrix and finding the number of possible totals which can get  length k I may be wrong to or correct but I finding to implement this in code neatly too.

That is if (0,1,2,1,3,4,1,2)

The number of possible 2 this are 

0+2=2

0+2=2

1+1=2

1+1=2

1+1=2

So a total of 5 , 2 length path with respect to that vertex moving from left to right

Again if number of 3 length paths 

Moving left to right

0+3=3

1+2=3

1+1+1=3

1+2=3

2+1=3

2+1=3

1+2=3

1+2=3

Total 8 paths of length 3

Until maximum possible length path from that vertex with respect to that graph.

Their is a mistake in the above logic is if the length paths intersection in some edges the path length will decrease so need to be careful so it looks difficult for me.

But I may be wrong in logic need help."

I am trying too

Kind help please your answer will be acknowledged 

Kind help 

Kind help someone please 

I have quite a big code with lot of functions how to convert all together to python in one go 

Or any other way of advice 

As recoding is difficult. Can you help with a small sample program with 2 simple functions returning values

Graph theory and it's algorithms, linear algebra , have used in my program codings mainly 

In small function kind take to a create a small graph find allpairshortestpath 

It would help to understand how it converts

Please help sorry to disturb in your busy schedule

 Function given like this

J:=0

F:=proc(operation)

J:=0;

for i to n do
    for j from i + 1 to n do if A(i, j) = 1 then J := J + mod(X (operation) Y); end if; end do; end do;
end proc;

I have simply put the word operation their to explain

If call the fuction F by F("m")  m means multiple the I should get * operator should multiple and it should multiply

If I call function F by F("A") A means Addition then should get + operator should add and it should do +

If I call function F by F("S")  S means Subtraction then should get - operator should subtract and it should do -

mod means absolute value always

 suppose i have outputs of several functions retured as variables float

A , B , C , D ,E , F , G , H , I , J , K ,L,M ,N , O, P,Q

I run the functions several times that all the function are run even if one is run 

so for each run I get a row of the matrix M in that order how to create from that outputs

each output is appended as next row in the same way to the matrix in the same order

Then I want the final matrix after all run to me exported to excel