Markov Chain in a Graph
So far, we’ve mostly used small matrices, with a clear geometrical meaning: \(2\times 2\) matrices transform the Cartesian plane, and \(3\times 3\) matrices transform the entire Cartesian space. What about yet bigger matrices? Fortunately, they may still have a geometrical meaning of their own. Indeed, in graph theory, they may help design a weighted graph, and model a stochastic flow in it. This makes a Markov chain, converging to a unique steady state. This has a practical application in modern search engines on the Internet .