Is there any function that gives the smallest basic cycles of a Graph?

Is there any function that gives the smallest basic cycles of a Graph.i have use cyclebasis but the cycles are not the smallest

[Dyuman Joshi]

What do you mean by smallest basic cycle?

[Antonio Agüero Ramón-Llin]

Less edges or elements

[Antonio Agüero Ramón-Llin]

The function cyclebasis gives you the basic cycles but they dont have to be the smallest

[Catalytic]

The function cyclebasis gives you the basic cycles but they dont have to be the smallest

Do you have an example of that? They should be, I think.

[Antonio Agüero Ramón-Llin]

I found an example i will post it tomorrow from my computer.

The function Cyclebasis gives independent cycles but not the smallest

[Antonio Agüero Ramón-Llin]

Graph example

[Antonio Agüero Ramón-Llin]

xni(1)=1; xnf(1)=2; xt(1)=1.2

xni(2)=2; xnf(2)=3; xt(2)=0.5

xni(3)=3; xnf(3)=4; xt(3)=1.0

xni(4)=3; xnf(4)=5; xt(4)=1.0

xni(5)=5; xnf(5)=1; xt(5)=0.5

xni(6)=5; xnf(6)=6; xt(6)=1.0

xni(7)=6; xnf(7)=7; xt(7)=1.0

xni(8)=7; xnf(8)=8; xt(8)=1.0

xni(9)=1; xnf(9)=9; xt(9)=1.2

xni(10)=9; xnf(10)=6; xt(10)=0.5

xni(11)=7; xnf(11)=10; xt(11)=0.5

xni(12)=9; xnf(12)=10; xt(12)=1.2

The graph is defined by s=xni; t=xnf

try to apply cyclebasis and check the cycles

[Antonio Agüero Ramón-Llin]

s=xni; t=xnf;

G=graph(s,t);

Cy=cyclebasis(G)

results :

Cy =

3×1 cell array

{[ 1 2 3 5]}

{[1 5 6 7 10 9]} (the "smallest" independent cycles should have the three of them 4 vertex, this one has 6 is also independent but not "smallest")

{[ 1 5 6 9]}

Answer 1

[Matt J]

This might help,

https://www.mathworks.com/matlabcentral/fileexchange/73630-spatialgraph2d?s_tid=srchtitle

[Antonio Agüero Ramón-Llin]

I think this function gives what i Need graphically, but i need to know which are the vertex of all the smallest basic cycles.

I need to have as output of the function the vertex of rachee cycle. As all cycles or Cyclebasis give

[Matt J]

Yes. Why do you think you don't have that?

[Antonio Agüero Ramón-Llin]

Is there an array with those cycle and vertex?

[Matt J]

Yes, the polyshape method gives you polyshapes for each region. Polyshape objects contain the vertices, e.g.,

s = [1 1 1 2 3 3 4 4 5 6 7 6 8 9 10 10 12 12 13 14 15 16 17 17 18 19 20 21 20 25];
t = [2 8 18 3 4 23 5 21 6 7 8 11 9 10 11 12 14 13 15 18 16 17 18 25 19 20 1 22 24 26];
G = graph(s,t);

x = [0.5 0 0 0 0.5 1 1.5 2 3 3 3 5.5 6 4 6 6 4 3 2 0.5 -1 -2 -1 1.5 4.5 4.5];
y = [0 0.5 1 1.5 2 2 1.5 1 1 1.5 2 1 0.5 0.5 0 -1 -1 -0.5 -1 -1 1 0.5 0.5 -0.5 -0.5 0];

obj=spatialgraph2D(G,x,y);


pgon=obj.polyshape;

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

pgon(1).Vertices,

ans = 6×2

0.5000 0 0 0.5000 0 1.5000 0.5000 2.0000 1.0000 2.0000 2.0000 1.0000

plot(pgon)

[Antonio Agüero Ramón-Llin]

To obtain coordinates of vertices is pgon(1).vertices

And to obtain the vertices numbers?

[Matt J]

You can call with 2 outputs,

[pgon,nodeNumbers]=obj.polyshape;