Fig. 5.

Directed Graph Plot illustrating the characteristics of our matrix. The plot visually represents the matrix as a directed graph, where nodes represent different states, and the edges between the nodes represent non-zero transition probabilities. The critical features depicted in the graph plot are the aperiodicity and irreducibility of the matrix. The strongly connected network nodes in the graph plot indicate that all states within the system are interconnected, with paths or transitions between them. This implies that each state can influence or be influenced by other states in the system. The edges, represented as arrows, symbolize the non-zero transition probabilities between states. These edges capture the likelihood or probability of transitioning from one state to another within the system.