The presentation of kingship in Hamlet is complicated by the fact that the king, who is also the character who has the most to say about kingship as a concept, is a usurper and a murderer. Claudius says that he is not afraid of Laertes because:
There's such divinity doth hedge a king,
That treason can but peep to what it would,
Acts little of his will.
However, if this were entirely true, Claudius would not have been able to commit treason by killing the rightful king and taking his crown. Claudius's constant attempts to reinforce the dignity of kingship through his use of hyperbole come to seem somewhat desperate. He even refers to himself in the third-person as "the king," a rhetorical technique intended to emphasize the dignity of his position. However, it also has the effect of detaching the man from the role, drawing attention to the fact that Claudius's crime does not diminish the conceptual majesty of kingship.
Those who wish to flatter the king adopt the same perspective. Among these are Rosencrantz and Guildenstern, the former of whom says to Claudius:
The cease of majesty
Dies not alone; but, like a gulf, doth draw
What's near it with it: it is a massy wheel,
Fix'd on the summit of the highest mount,
To whose huge spokes ten thousand lesser things
Are mortised and adjoin'd; which, when it falls,
Each small annexment, petty consequence,
Attends the boisterous ruin. Never alone
Did the king sigh, but with a general groan.
This is the idea that Thomas Hobbes was soon to express in his Leviathan (1651). The king is not simply another individual, however powerful. His fate is profoundly connected to that of all his subjects, as Rosencrantz illustrates with his metaphor of the wheel. The irony here is that, while Shakespeare agrees with the concept, he is showing that Denmark has descended into chaos precisely because the wheel has already fallen from the summit with the murder of King Hamlet.