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Plot Markov chain directed graph

`graphplot(mc)`

`graphplot(mc,Name,Value)`

`h = graphplot(___)`

`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 `mc`

,`Name,Value`

)`Name,Value`

pair arguments. Options include highlighting transition probabilities,
communicating classes, and class properties of recurrence/transience and period.
Also, you can plot the condensed digraph instead, with communicating classes as
*supernodes*.

To produce the directed graph as a MATLAB

^{®}`digraph`

object, and utilize additional functions of that object, enterG = digraph(mc.P)

For readability, the

`'LabelNodes'`

name-value pair argument allows lengthy node labels to be turned off and replaced by 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 outdegreee)

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.

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