This is a topic that has interested me for a while: it seems to be taken as granted that a listener knows what is meant by a "strong" and a "weak" ruler, and while I understand the idea in generalities I'd be really interested in specifics (especially if there are any books that contrast the politics of the realm between strong and weak rulers).
The rule of King Matthias of Hungary especially interests me, because he is regarded as a very strong ruler but everything rapidly fell apart after he died.
First, a question, are you interested in medieval Hungary or power structures or both or some other stuff, too?
In a very practical sense, if you are a king, you are powerful, otherwise you wouldn't be king. Look at the Carolingians, and the Normans, and Ottomans, and pretty much every other ruling group or family from the middle ages. Ruling = powerful; no longer ruling = no longer powerful. There were varying levels of power. You could rule a kingdom or a duchy or an earldom or a barony or a diocese or any other division of land. This power was most explicitly represented through military might and wealth (primarily through landownership). If you had a better or bigger army, you got more power. If you had more land, you (usually) had a bigger population to get your army from. The Capetians did this slowly in France, the Normans did it quickly in England, and the Crusaders had success and failure in the Holy Land. If a ruler had power through military might, it allowed him (because it was usually him) to more easily accomplish any social, political, or religious goals. Frederick II didn't agree with the pope's policies, so he went down and kicked him out. The Avignon papacy developed because the French monarch didn't like the current policies of the Church.
Here are some books that discuss power structures in medieval Europe:
Giovanni Tobacco. The struggle for power in medieval Italy : structures of political rule. (Cambridge, 1989)
Colin Imber. The Ottoman Empire, 1300-1650 : the structure of power (Palgrave, 2002)
Joyce Hill and Mary Swan. (eds.). The community, the family and the saint : patterns of power in early medieval Europe : selected proceedings of the International Medieval Congress, University of Leeds, 4-7 July 1994, 10-13 July 1995 (1998)
David Loades. Tudor government : structures of authority in the sixteenth century (Blackwell, 1997)
Robert C. Figueira. Plenitude of power : the doctrines and exercise of authority in the Middle Ages : essays in memory of Robert Louis Benson (Ashgate, 2006)
Frans Theuws and Janet L. Nelson (eds.). Rituals of power : from late antiquity to the early Middle Ages (Brill, 2000)
Thomas N. Bisson (ed.). Cultures of power : lordship, status, and process in twelfth-century Europe. (U Penn, 1995)
Hope this helps a little. Happy reading!