Given $n \in \mathbb{N}$ and a distribution over all possible simple graphs on $[n]$, $f: 2^{[N]} \to [0, 1]$, let $\mathcal{G}_f$ denote the (random) graph following the distribution $f$.
We have three related quantities:
1. expected global transitivity (i.e., expected global clustering coefficient)
Given a simple graph $G = (V, E)$, let $t_G$ denote the number of triangles in $G$ and $w_G$ the number of wedges in $G$ (for each triplet $\{x, y, z\} \in V$, there are three potential wedges and one single potential triangle). The global transitivity (a.k.a. global clustering coefficient) of $G$ is $gcc(G) := 3t(G) / w(G)$, and thus the expected global transitivity of $\mathcal{G}_f$ is $$Q_1(\mathcal{G}_f) = \sum_{G} f(G) gcc(G).$$
2. the ratio between the expected numbers of triangles and wedges
As the name suggests (and with necessary rescaling), $$Q_2(\mathcal{G}_f) = \frac{3 \sum_{G} f(G) t(G)}{\sum_{G} f(G) w(G)}$$
3. mean-local transitivity
Given a simple graph $G = (V, E)$ and $v \in V$, the local transitivity (a.k.a. local clustering coefficient) of $v$ is $lcc(v; G) := |\{x, y \in N(v): (x, y) \in E\}| / |\{x, y \in N(v)\}|$, where $N(v)$ is the neighborhood of $v$. When $\{x, y \in N(v)\}$ is empty (i.e., $|N(v)| < 2$), we let $lcc(v; G) = 0$. Then we define the mean-local transitivity of $\mathcal{G}_f$: $$Q_3(\mathcal{G}_f) = \sum_{G} f(G) \frac{\sum_{v \in [n]} lcc(v; G)}{|\{v \in [n]: |N(v)| \geq 2 \}|}.$$
Can we claim that $Q_1$ approaches $Q_2$ and $Q_3$ asymptotically? There is a related question on this site Expected global clustering coefficient for Erdős–Rényi graph. But this question only deals with $G(n, p)$. I wonder what we can obtain for more general cases, at least for the cases where each edge exists independently.