Consider the $G(n,p)$ random graph model where $n$ is a ``large'' positive integer and $p\in (0,1)$.  We may equip every realized random graph $G$ with its shortest path distance, making it into a (random) metric space $(G,d_G)$.  Since $G$ is finite then $(G,d_G)$ is [doubling][1]; we dente

Are the known estimates for the expected doubling constant of such a random graph?


  [1]: https://en.wikipedia.org/wiki/Doubling_space