# graphs – Power of adjacency matrix

Let $$G$$ be a weighted graph with a weight function $$w longrightarrow mathbb{R}^{+}$$. Let $$G’$$ denotes the weighted matrix with adjacency matrix

$$A_{G’} = sum_{i=0}^{k} (xA)^{i}$$

where $$k$$ is integer and $$x$$ is a variable.

I am not getting what is $$A_{G’}$$ matrix? Is it contains all walks of length $$k$$ or is it something else?