Stationary distribution for different types of graph - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T20:30:10Z http://mathoverflow.net/feeds/question/122779 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/122779/stationary-distribution-for-different-types-of-graph Stationary distribution for different types of graph Fatime 2013-02-24T05:43:42Z 2013-02-24T19:55:54Z <p>This is a follow-up question to posts:</p> <p><a href="http://math.stackexchange.com/questions/311147/stationary-distribution-for-directed-graph" rel="nofollow">Stationary distribution for directed graph</a></p> <p><a href="http://math.stackexchange.com/questions/312626/stationary-distribution-for-different-types-of-graph/313201#313201" rel="nofollow">Stationary distribution for different types of graph</a></p> <p>The definition of stationary distribution in wikipedia:<a href="http://en.wikipedia.org/wiki/Markov_chain#Steady-state_analysis_and_limiting_distributions" rel="nofollow">Steady-state analysis and limiting distributions</a></p> <p>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 ?</p> <p>If not, what is the difference for each case?</p> <p>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.</p> <p>Thanks</p>