I'm having trouble finding any other references to a notion of a dimension of a graph which is based on howthe number of vertices which can be reached through a

I'm having trouble finding any other references to a notion of a dimension of a graph which is based on howthe number of vertices which can be reached through a path of a given length increases with the length. I'm finding things like, a dimension of a graph as the minimum dimension of euclidean space where the vertices can be placed and have each edge have length 1, and another thing which seems closer which is based on a metric from the graph, but that is based on the idea of a metric basis, which I don't think is equivalent (in it, a subgraph can have a higher dimension than the graph it is a subgraph of, which I don't think is the case in the version mentioned in this blog post. And one example I'm p sure has finite dimension in the blog post version, but infinite dimension in the other thing, so, I'm p sure they are different things). Does anyone have any non wolfram references for the notion of the dimension of a graph as is explained in the post linked?