Isogeny graph (general definition, degree, duals...).
Starting vertex (Bröker's algorithm).
Isogeny Volcanos: Sutherland might be a good source https://arxiv.org/abs/1208.5370.
Supersingular isogeny graphs
Size, everything is defined over GF(p^2). (*as long as the degree divides (p+1)^2 or (p-1)^2).
Random walks are probably the best motivation to define Ramanujanness, and are directly applicable to cryptography. A (perhaps too large) source is Hoory-Linial-Wigderson.
Consequence from Ramanujan + random walk convergence: O(log p) diameter.