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Plot Markov chain directed graph

`graphplot(`

creates a plot of the directed graph (digraph) of the discrete-time Markov chain `mc`

)`mc`

. Nodes correspond to the states of `mc`

. Directed edges correspond to nonzero transition probabilities in the transition matrix `mc.P`

.

`graphplot(`

uses additional
options specified by one or more name-value arguments. Options include highlighting transition probabilities, communicating classes, and specifying class properties of recurrence/transience and period. Also, you can plot the condensed digraph instead, with communicating classes as `mc`

,`Name,Value`

)*supernodes*.

`graphplot(`

plots on the axes specified by `ax`

,___)`ax`

instead of the current axes (`gca`

) using any of the input argument combinations in the previous syntaxes. The option `ax`

can precede any of the input argument combinations in the previous syntaxes.

To produce the directed graph as a MATLAB

^{®}`digraph`

object and use additional functions of that object, enter:G = digraph(mc.P)

For readability, the

`'LabelNodes'`

name-value pair argument allows you to turn off lengthy node labels and replace them with node numbers. To remove node labels completely, set`h.NodeLabel = {};`

.To compute node information on communicating classes and their properties, use

`classify`

.To extract a communicating class in the graph, use

`subchain`

.The condensed graph is useful for:

Identifying transient classes (supernodes with positive outdegree)

Identifying recurrent classes (supernodes with zero outdegree)

Visualizing the overall structure of unichains (chains with a single recurrent class and any transient classes that transition into it)

[1]
Gallager, R.G. *Stochastic Processes: Theory for Applications.* Cambridge, UK: Cambridge University Press, 2013.

[2]
Horn, R., and C. R.
Johnson. *Matrix Analysis.* Cambridge, UK: Cambridge University Press,
1985.

[3]
Jarvis, J. P., and D.
R. Shier. "Graph-Theoretic Analysis of Finite Markov Chains." In *Applied Mathematical
Modeling: A Multidisciplinary Approach.* Boca Raton: CRC Press, 2000.