Well, it appears that proximate cause of this conflict boils down to two thing, control of the Beruit airport and Hezbollah’s communications system:

It has been announced by all sides that today is the first day of the civil war in Lebanon. This has been building with the steady assassination of political leaders since the conclusion of the war in 2006. Hezbollah is not happy, and all of a sudden the government of Lebanon has access to some very accurate intelligence.

It started with a tip regarding airport security and the means by which Iran was reportedly flying in military supplies to Hezbollah. It didn’t go over well with the militia when the government announced they were going to seize control of a security camera system in the Beruit airport. That was followed by the removal of the head of airport security, a member of Hezbollah.

It’s not particularly surprizing that this would lead to violence. You are talking about the supply lines and the communications network of Hezbollah, which are crucial to them tactically.

Hezbollah has now appeared to lave largely withdrawn from west Beruit, but they appear to still be aggressively confronting Walid Jumblatt’s pro government Druze forces east of the city.