在Matlab中求解图中节点的影响 [英] Solve for influence of nodes in graph in Matlab

问题描述

我有一个有5个节点的定向未加权图：x1到x5。边缘是：

  x1-> x3 
 x2-> x1 
 x2-> x5 
 x3-> x2 
 x3-> x4 
 x4-> x5 
 x5-> x2 
  pre> 
 
 
我想解决这个对应于图的方程组：
 
 
  x1 = alpha * x2 
 x2 = alpha *（x3 + x5）
 x3 = alpha * x1 
 x4 = alpha * x3 
 x5 = alpha *（x2 + x4）
 x1 + x2 + x3 + x4 + x5 = 1 
  
如何设置在Matlab中解决这些方程并解决？我想要x1到x5这些方程的值。
解决方案
以下是适用于我的解决方案： p> 
 
 
  syms abcde alpha 
 S = solve（-a + alpha * b == 0，-b + alpha * c + alpha * d == 0，alpha * ac == 0，alpha * cd == 0，... 
 alpha * de == 0，a + b + c + d + e == 1）; 
 S = [S.a S.b S.c S.d S.e S.alpha] 
  
 
I have a directed, unweighted graph with 5 nodes: x1 through x5. The edges are:
x1->x3
x2->x1
x2->x5
x3->x2
x3->x4
x4->x5
x5->x2
I want to solve this set of equations corresponding to the graph:
x1 = alpha * x2
x2 = alpha * (x3 + x5)
x3 = alpha * x1
x4 = alpha * x3
x5 = alpha * (x2 + x4)
x1 + x2 + x3 + x4 + x5 = 1
How can I set up these equations and solve in Matlab? I want the values of x1 through x5 for which the equations hold.
解决方案
Here is the solution that worked for me:
syms a b c d e alpha
S = solve(-a+alpha*b==0, -b+alpha*c+alpha*d==0, alpha*a-c==0, alpha*c-d==0, ...
alpha*d-e==0, a+b+c+d+e==1);
S = [S.a S.b S.c S.d S.e S.alpha]


                        
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