A NEW fad is sweeping across Silicon Valley, causing excitement, confusion and hyperbole not seen since the dotcom bubble. It began in May, when Mark Zuckerberg, ten days after turning 23, took the stage in a San Francisco warehouse and announced that he was opening up Facebook, the social network he founded at Harvard University, to outside programmers. Anyone can now build little programs, or “widgets”, into the network. To illustrate his idea, Mr Zuckerberg projected onto the wall behind him a “social graph”—a pattern of nodes representing Facebook users and the links among them.

Since then Facebook and the idea of the social graph have become the favourite, if not the only, topic of conversation among the valley's geeks, venture capitalists and internet moguls. Mr Zuckerberg compares his graphing of human connections to the work of Renaissance mapmakers. Facebook is growing furiously and may catch up with MySpace, the biggest social network. Outside programmers have added about 5,000 widgets.

One of Facebook's investors estimates the social network's revenues in 2007 at only $100m, mostly from selling ad space, with tiny profits. Nevertheless, the internet's giants—Yahoo!, Microsoft and Google—are offering to buy Facebook or a stake in it for a price that would value the firm at many billions. At a Facebook conference on “Graphing social patterns,” panellists said the firm may be worth $100 billion and that it is the new Google.

How much of this is hype? Facebook has made two genuine breakthroughs. The first was its decision to let outsiders write programs and keep all the advertising revenues these might earn. This has led to all kinds of widgets, from the useful (comparing Facebookers' music and film tastes, say) to the inane (biting each other to become virtual zombies). The entire internet industry reckons this was clever and is planning to copy it. This week MySpace said it would open its site to outside programmers. Google, which owns Orkut, a social network extremely popular in Brazil and parts of Asia, is expected to do the same soon. Facebook's second masterstroke is its “mini-feed”, an event stream on user pages that keeps users abreast of what their friends are doing—uploading photos, adding a widget and so on. For many users, this is addictive and is the main reason they log on so often. Jerry Michalski, a consultant, calls the mini-feed a “data exhaust” that gives Facebook users “better peripheral vision” into the lives of people they know only casually. This mini-feed is so far the clearest example of using the social graph in a concrete way.

Silicon Valley's craze for the “social graph”, however, is overdone. The term has been around in computer science for decades, says Eric Schmidt, Google's chief executive, so it is puzzling that Mr Zuckerberg should get any special credit for using it. “We have address books, and the sum of the address books is the social graph,” he says. Companies such as Plaxo, which help to synchronise address books, and Google itself, which has a primitive address book in its web-mail service, plan to turn these books into fully fledged social graphs that can do useful and productive things, perhaps including new variants of mini-feeds.

This analogy to address books points to an important limitation for social networks, such as Facebook, compared with older sorts of network, such as the postal or telephone systems. These benefit from Metcalfe's Law, which says that the value of a network is proportional to the square of the number of its users. In other words, the more people have phones, the more useful they become. This “network effect” leads to rapid adoption and puts up barriers for new entrants.

But unlike other networks, social networks lose value once they go beyond a certain size. “The value of a social network is defined not only by who's on it, but by who's excluded,” says Paul Saffo, a Silicon Valley forecaster. Despite their name, therefore, they do not benefit from the network effect. Already, social networks such as “aSmallWorld”, an exclusive site for the rich and famous, are proliferating. Such networks recognise that people want to hobnob with a chosen few, not to be spammed by random friend-requests.

This suggests that the future of social networking will not be one big social graph but instead myriad small communities on the internet to replicate the millions that exist offline. No single company, therefore, can capture the social graph. Ning, a fast-growing company with offices directly across the street from Facebook in Palo Alto, is built around this idea. It lets users build their own social networks for each circle of friends.

So are Facebook and its graph really worth many billions? From an advertiser's point of view, says Rishad Tobaccowala, the boss of Denuo, the new-media unit of Publicis Groupe, an advertising company, Facebook is so far anything but the new Google. The search giant does have traditional network effects in its advertising system, he says: it aggregates advertisers and sends them to potential customers who have expressed specific intentions by typing search queries. But Facebook has only “large crowds who are communicating without expressing specific interests”, says Mr Tobaccowala. On Google, advertisements are valued; on Facebook they are an annoyance that users ignore.

Facebook might nonetheless be suited for other sorts of marketing. Reuben Steiger, the founder of Millions of Us, a marketing agency for social networks and virtual worlds, says that brands need to design “experiences” that use the social graph to engage groups of friends. If a wrestling association, say, wants to drum up ticket sales for an upcoming bout, it could build a widget that turns users into wrestlers and lets them fight bad guys and win gifts, while making them aware of the brand and the match.

But that possibility hardly justifies the sorts of valuations bandied around for Facebook and other social networks. Such valuations, indeed, may reflect a misunderstanding of the social graph. For bigger companies such as Google, the graph is simply the web of links among its many users. It can be used to make existing services more useful. But Google increasingly views such utilities as “features, not products,” says Sergey Brin, its co-founder. Facebook, like many hot start-ups in Silicon Valley, has some fantastic features, but maybe not much more.