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Stationary distribution for directed graph

Stationary distribution for different types of graph

The definition of stationary distribution in wikipedia:Steady-state analysis and limiting distributions

Are stationary distributions of graphs with every property(for example directed or undirected, strongly connected or sparse, periodic or aperiodic)proportional to eigenvector corresponding to eigenvalue 1 ?

If not, what is the difference for each case?

I know when the graph is undirected strongly connected and aperiodic, there is a unique stationary distribution equal to the degree of the vertex divided by the overall degree of nodes.But I don't Know how is it for other type of graph.

Thanks
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This is a follow-up question to posts:

Stationary distribution for directed graph

Stationary distribution for different types of graph

Are stationary distributions of graphs with every property(for example directed or undirected, strongly connected or sparse, periodic or aperiodic)proportional to eigenvector corresponding to eigenvalue 1 ?

If not, what is the difference for each case?

I know when the graph is undirected strongly connected and aperiodic, there is a unique stationary distribution equal to the degree of the vertex divided by the overall degree of nodes.But I don't Know how is it for other type of graph.

Thanks
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Stationary distribution for different type types of graph
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