# Facebook uses "Good Will Hunting" math for a bigger, badder network

(MoneyWatch) COMMENTARY In a story of business imitating art imitating life, Facebook (FB) is working in an area that recalls the movie "Good Will Hunting." No, neither Matt Damon nor Ben Affleck has gone to work for the social media network and Mark Zuckerberg didn't get a job as a janitor at MIT. (He went to that small liberal arts college up the road.) However, Facebook has deeply embedded into its expanding network the same type of math - graph theory - which Damon's character did in the movie. And a recent patent gives it a strong advantage in using the power of this study in analyzing and optimizing interactions, possibly locking other companies such as Google (GOOG) and Twitter out of effectively treating their social networks as mathematical graphs.

Graph theory seems simple on the surface: A bunch of dots, called nodes, connected by lines called edges. It's the study of connecting entities of one sort of another (objects, concepts, or anything else) in pairs. The result is a latticework of nodes and edges. Where things get interesting is in how you can analyze the way influences and interactions can run throughout a given graph. Biology, computer science, linguistics, chemistry, and physics are just a few areas in which graph theory becomes important.

People are math, too

A social graph is a collection of people, companies, institutions, and even concepts (people connecting to pages or sites about genres of music or fashion designers, for example) and the ways they connect to each other. Graph theory makes a powerful tool to analyze the social graph, understand how nodes influence each other, optimize operations, and even efficiently manage advertising and marketing to the users.

That's where patent 8,185,558, called Automatically generating nodes and edges in an integrated social graph, comes into play. Filed in April 2010, the patent was granted today.

Although I'd typically include the main independent claim that shows the actual legally protected concept, it is long and convoluted. Instead, here's my summary: Facebook can model a social network as a mathematical graph for analysis by treating people, organizations, companies, and even abstract concepts as sets of nodes and the paired connections among them as the edges. The company can further scan content associated with each node, finding matches to create new edges or even new concept nodes.

Automating the social automaton

In other words, Facebook can use math to analyze an existing social network and generate new connections among users, organizations, and concepts to further fill out the network. The obvious use is to suggest such things as interests, pages, potential online friends, and brands to users, based on the content of their posts, shared links, profiles, and even private messages and emails.

But Facebook could also suggest prospects to companies and advertisers, or even help discover new service and product areas for its business partners. Furthermore, the company can then employ all of graph theory to aid in efficient analysis, design, and optimization of the network.

The patent doesn't prohibit Google, Twitter, or any other company from using graph theory in their social networks. But it puts a road block in the way of their automatically generating the graph to analyze, and certainly from using graph theory to expand and extend their networks.