In my campaign, players are attempting to stop a murder as their long-term goal. In essence, this makes the victim the central component of the web (or classically, as the central point in the web where all the spokes meet.)
From the center, work out the closest associates of that character. For this campaign, I start with Count Vilsador, the target of the murder. Immediately next to him in the web is Maxwell, his Brother, his Father, and his Steward. Directly after come business and political contacts. I then fleshed out my web by adding more contacts to the people the Count knew.
The web needs more info than just a nice picture of who knows who, who wants to stab who with a pitchfork, and so on. Actually knowing the nature of the people involved, their goals, desires and ways of making money and methods is the brunt of the work. Staring at my web will not reveal that Drogon is an information broker, that Feldas is a sniveling coward, or that Reed is an upstanding honest man. It also does not fill in any player goals.
Web of Intrigue Advantages:
Easy to spot who is connected to whom.
Dynamic. Web can change as players affect the social situations they are in.
Documents relationships concretely.
Groups NPCs into factions fairly easily.
Web of Intrigue Disadvantages:
Hard to reference in game.
Larger webs get exponentially more complicated.
Players can be stranded without a good social contact.