How Vopenka's principle implies Semi-Weak Vopenkas principle? Let's consider 2 large cardinal axioms, the Vopenka's principle (VP)
which says that Ord cannot be fully embedded into Graphs and
SWVP which says, that the equivalence $Hom(G(\alpha),G(\alpha'))=\emptyset\Leftrightarrow \alpha<\alpha'$ doesn't hold for any sequence (indexed by Ord) of graphs:
$$\langle G(\alpha) | \alpha\in \text{Ord}\rangle$$ 
My question is, how can I see that VP implies SWVP as noted here?
 A: Assume that SWVP fails, as witnessed by a sequence of graphs $\langle \langle G_\alpha; E_\alpha \rangle : \alpha < \text{Ord}\rangle$ such that for all $\alpha, \beta \in \text{Ord}$ there is a homomorphism $\langle G_\alpha; E_\alpha\rangle \to \langle G_\beta; E_\beta\rangle$ if and only if $\alpha \ge \beta$.
Note that the cardinalities of the graphs must be unbounded: otherwise there would be two isomorphic graphs on the sequence.  So by thinning the sequence, we may assume that the cardinality of $G_\alpha$ is a strictly increasing function of $\alpha$.
Then letting $A_\alpha = \{\langle x,y \rangle \in G_\alpha \times G_\alpha : x \ne y\}$ and letting $B_\alpha$ be a rigid binary relation on $G_\alpha$, the sequence $\langle\langle G_\alpha; E_\alpha, A_\alpha, B_\alpha\rangle : \alpha \in \text{Ord}\rangle$ is a counterexample to VP.
Alternatively, the implication from VP to SWVP becomes trivial using the following equivalent form of VP: given any sequence of graphs $\langle \langle G_\alpha; E_\alpha \rangle : \alpha < \text{Ord}\rangle$, there is a homomorphism $\langle G_\alpha; E_\alpha\rangle \to \langle G_\beta; E_\beta\rangle$ for some $\alpha, \beta \in \text{Ord}$ such that $\alpha < \beta$.  This follows from the set-theoretic characterization of VP (see Kanamori, The Higher Infinite).  In this characterization, $\alpha$ and $\beta$ arise as the critical point and image of the critical point respectively of an elementary embedding between rank initial segments of the universe.
