How to make Network/nodal analysis and value distribution in MATLAB?

Hi,

I have 8 nodes, where each node is connected to 3 other nodes. Each node have a numerical value (positive or negative). The aim is to make negative nodes 0 by take positive values from connected nodes. (each nodes will be indicated by a variable, eg: a, b, c..... and values will be generated from a simulink model)

I found the solution as:

• Positive and negatives nodes have to be seperated into array
• Take the sum of all positive nodes coming to the negative node and sort it based on the differerence of negative node value to the sum
• The negative node on the top take positive value from the connected node with highest positive number.
• Update the nodal values
• Now above step is repeated again.

I am not sure how to do this, and I need help with this. for checking, these are some reference values. I hope some experienced community members can help me.

Node connections are:

Node 1 - 2,3,8; Node 2 - 1,4,8 ; Node 3 - 1,5,8 ; Node 4 - 2,6,7 ; Node 5 - 3,7,6 ; Node 6 - 4,5,7 ; Nide 7 - 4,5,6 ; Node 8 - 1,2,3

Node values:

Node 1 = -8.95 ; Node 2 = 4.62 ; Node 3 = 14.07 ; Node 4 = -2.69 ; Node 5 = -9.14 ; Node 6 = -0.83 ; Node 7 = 2.2 ; Node 8 = 11.72

Answer 1

[Chunru]

"graph" can be used for such problem.

Node connections are:

Node 1 - 2,3,8; Node 2 - 1,4,8 ; Node 3 - 1,5,8 ; Node 4 - 2,6,7 ; Node 5 - 3,7,6 ; Node 6 - 4,5,7 ; Nide 7 - 4,5,6 ; Node 8 - 1,2,3

s = [1 1 1 2 2 3 3 4 4 5 5 6 ]';    % undirected graph
t = [2 3 8 4 8 5 8 6 7 7 6 7 ]';
g = graph(s, t);
plot(g)

Node values:

Node 1 = -8.95 ; Node 2 = 4.62 ; Node 3 = 14.07 ; Node 4 = -2.69 ; Node 5 = -9.14 ; Node 6 = -0.83 ; Node 7 = 2.2 ; Node 8 = 11.72

v = [-8.95; 4.62; 14.07; -2.69; -9.14; -0.83; 2.2; 11.72]'

v = 1×8

-8.9500 4.6200 14.0700 -2.6900 -9.1400 -0.8300 2.2000 11.7200

Change values:

The following is a simple approach. Not sure if it always give a solution.

while any(v<0)
    % find the minimum of v
    [vmin, imin] = min(v);
    % find the neighbors of imin
    n = neighbors(g, imin);
    % borrow values from the neighbor nodes with highest value
    [vmax, imax] = max(v(n));
    borrowvalue = min(-vmin, vmax);
    v(imin) = v(imin) + borrowvalue;
    v(n(imax)) = v(n(imax)) - borrowvalue;
    fprintf("imin=%d  imax=%d  ", imin, n(imax))
    fprintf("%8.2f ", v)
    fprintf('\n')
end

imin=5  imax=3  

   -8.95     4.62     4.93    -2.69     0.00    -0.83     2.20    11.72 

imin=1  imax=8  

    0.00     4.62     4.93    -2.69     0.00    -0.83     2.20     2.77 

imin=4  imax=2  

    0.00     1.93     4.93     0.00     0.00    -0.83     2.20     2.77 

imin=6  imax=7  

    0.00     1.93     4.93     0.00     0.00     0.00     1.37     2.77 

[Shemin Sagaria]

Hi,

Thank you so much for your answer. Its helps a lot. However, this approach is not working for other values. I checked this with 4 nodes

s = [1 1 2 2 3 3 4 4]';

t = [2 3 1 4 1 4 2 3]';

a = -21.28;

b = 11.15;

c = -8.42;

d = 24.55;

v = [a;b;c;d]'

[Chunru]

s = [1 1 2 3]';    % undirected graph
t = [2 3 4 4]';
g = graph(s, t);
plot(g)

v = [ -21.28;  11.15; -8.42; 24.55;]'

v = 1×4

-21.2800 11.1500 -8.4200 24.5500

sum(v)

ans = 6

k=1;
while any(v<0)
    %k
    % find the minimum of v
    [vmin, imin] = min(v);
       
    % find the neighbors of imin
    n = neighbors(g, imin);
  
    % To avoid dead lock
    if all(v(n)<=0)
        % randomly pick a neigbour
        idx_n = n(randi([1 length(n)], 1));
        % neighbour of neighbour
        n_n = neighbors(g, idx_n);
        
        [vmax, ii ] = max(v(n_n));
        ib = n_n(ii);
        v(idx_n) = v(idx_n) + v(ib);
        v(ib) = 0;
    end
    
    % borrow values from the neighbor nodes with highest value
    [vmax, imax] = max(v(n));
    borrowvalue = min(-vmin, vmax);
    v(imin) = v(imin) + borrowvalue;
    v(n(imax)) = v(n(imax)) - borrowvalue;
    fprintf("imin=%d  imax=%d  ", imin, n(imax))
    fprintf("%8.2f ", v)
    fprintf('\n')
    k=k+1;
    
    if k>100, break; end
end

imin=1  imax=2  

  -10.13     0.00    -8.42    24.55 

imin=1  imax=2  

    0.00    14.42    -8.42     0.00 

imin=3  imax=1  

    6.00     0.00     0.00     0.00