We consider the directed graph $G = ( S , A )$ where $$\left\{ \begin{array} { l } S = \{ 1,2,3,4 \} \\ A = \{ ( 1,2 ) , ( 2,1 ) , ( 1,3 ) , ( 3,1 ) , ( 1,4 ) , ( 4,1 ) , ( 2,3 ) , ( 3,2 ) , ( 2,4 ) , ( 4,2 ) , ( 3,4 ) , ( 4,3 ) \} \end{array} \right.$$ We assume that, when the point is on one of the vertices of the graph, it has the same probability of going to each of the three other vertices of the graph. We set $$J _ { 4 } = \left( \begin{array} { l l l l } 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \end{array} \right)$$ Express the transition matrix $T$ as a function of $J _ { 4 }$ and $I _ { 4 }$.
We consider the directed graph $G = ( S , A )$ where
$$\left\{ \begin{array} { l } S = \{ 1,2,3,4 \} \\ A = \{ ( 1,2 ) , ( 2,1 ) , ( 1,3 ) , ( 3,1 ) , ( 1,4 ) , ( 4,1 ) , ( 2,3 ) , ( 3,2 ) , ( 2,4 ) , ( 4,2 ) , ( 3,4 ) , ( 4,3 ) \} \end{array} \right.$$
We assume that, when the point is on one of the vertices of the graph, it has the same probability of going to each of the three other vertices of the graph. We set
$$J _ { 4 } = \left( \begin{array} { l l l l } 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \end{array} \right)$$
Express the transition matrix $T$ as a function of $J _ { 4 }$ and $I _ { 4 }$.