So lately I have been experimenting with different ways to attach a probability distribution on different aspects on graphs for different processes, to calculate various values that can be obtained from distributions (like expectations, variances, entropies, etc.). With regards to getting a distribution over the vertices, I was thinking of taking an approach along these lines:
- Obtain adjacency matrix $A$ of the graph $G$
- Normalise $A$ to get the stochastic matrix $\sigma_A$. Since $A$ is symmetric, row-wise and column-wise are related by a transpose so I will only choose column-wise.
- Let $\mathbb{P}[V(G)]$ be the components of eigenvector $p$ such that $[\sigma_A] p = p$
Would this be a good way of approacing it? The reason why I took this approach was because of the fact that it is similar to a PageRank-like process.