Network theory - Marc Samet

Transcriber: Andrea McDonough
Reviewer: Bedirhan Cinar

What does "going viral" on the internet really mean, and why does it happen so quickly? Why is a financial institution too big to fail? How does a virus in Africa end up in the United States in a matter of hours? Why are Facebook and Google such powerful companies at creating global connections? Well, in a word: networks.

But what are networks? Everyone knows about their social network, but there are all different kinds of networks you probably haven't thought about. Networks are collections of links which combine by specific rules and behaviors if they are alive. We say that networks are alive because they are in constant change. Over time, the connections within a network migrate and concentrate in new places, forming evolving structures.

How the evolution and concentration of constantly changing connections occurs is the subject of a whole discipline called network theory. We can think of networks as neighborhoods. Neighborhoods are defined by maps. A Google map demonstrates the relationship between locations in exactly the same fashion a network connects hubs and nodes, using streets as links to connect neighborhoods.

The reason a network can expand and evolve so quickly is based upon a mathematical concept called power functions. A power function is a mathematical amplification mechanism, which over specific and very small ranges, accelerates changes logarithmically. That is, a very small change in one parameter produces a huge change in another over a very specific range of values.

An example of how network structure emerges is the algorithm used by Google. As the number of links around a search term, say "friends", increases, connections begin to form among millions of different searches using the term "friend". What Google has cleverly accomplished is a real-time mathematical model for how to predict the emergence of growing connections among billions of search terms.

The algorithm Google derived collects the number of references to any search object. As references to a search object increase, the number of links also increases, creating a node. As the node increases in size, it eventually becomes a hub, which links to many nodes. Networks will continue to emerge as new ways of connecting and creating neighborhoods are defined.

Perhaps you can begin to see why networks are so powerful. As Google continues to collect the billions of daily searches, new clusters of links will rapidly emerge, forming additional and growing networks. Despite the logarithmic expansion of your network, the laws of six degrees of separation still apply. Therefore, if you explore a close friend or acquaintances in your Facebook network, everyone on average will be separated by six individuals or less, and a map of your social network will create neighborhoods linked by common connections among friends.