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Four Degrees of Separation?

Six Four Degrees of Separation?

The small-world phenomenon is the idea that a significant portion of the world belongs in one giant component. Pop culture has adopted the term six degrees of separation as the term that encapsulates this idea. This number “six” has stood for 50 years, ever since Milgram’s “small world” experiment. The world now is vastly different from 50 years ago, most notably the rise of technology and electronics. Internet has in 30 years transformed the landscape of humanity, it being a giant computer network that anyone with a computer can access. Social media has also transformed our lives – for most of us, it is our identity on the internet. But maybe, just maybe, social media also has the transcending power of  transforming our relationship networks – by giving us bridges of interconnections at the touch of a button.

The paper, Four Degrees of Separation, by Lars Backstrom et al. explores the world-scale social-network, Facebook. Their findings that “the average distance… is 4.74, corresponding to 3.74 ‘degrees of separation’, showing that the world is even smaller than we expected.” With a dataset of Facebook’s entire active user base (721 million nodes, 69 billion edges), this research is certainly comprehensive. Succinctly put, “when considering another person in the world, a friend of your friend knows a friend of their friend, on average.” The researchers explicitly note that this research was conducted on a graph of individuals – there are no “subscriptions” or pages that people may “like” included in the graph. Thus, an interpretation on their finding would be that it depicts the average distance of the human network, using the Facebook network as a proxy. We take note that this is slightly different from the Milgram experiments, since that experiment results in the length of a routing path, which is an upper bound for the average distance. This is because an individual sending the postcard to another does not know the shortest path, whereas this research utilizes graph algorithms (as well as a host of graph compression algorithms) to average the shortest distance between each set of two nodes for the entire network.

Novelly, this research   reaffirms our notion of a small world, confirming existence of the giant network consisting of all the people of the world. However, I feel we have to temper our expectations somewhat. The world may not be as interconnected as this paper indicates. I maintain this position based upon the research Marlow et. al. has conducted on the strength of friendship ties on Facebook. In it, they defined three categories of friend relationships: mutual, one-way, maintained. What is striking is the relatively small size of each of these relationships. With approximately a network of 400 (corresponding to an user on Facebook with 400 friends) , maintained relationships numbers 40, one-way, 20 and reciprocal, 10. Thus, only approximately 10% of all “friends” for a Facebook user with 400 friends can be categorized as in-touch. The rest, maybe acquaintances or distant friends. Or perhaps even enemies, as the saying “keep your friends close, but your enemies closer” goes. Thus, this proposed “Four Degrees of Separation” may be more diluted than we first imagine. Maybe it is only four degrees if we accept even the weakest of weak edges as a friendship relation.

A little known fact is Milgram actually offered an opposing interpretation of what “six degrees of separation” meant. He spoke of also interpreting the results to mean we are really  “six worlds apart”. The researchers Backstrom et. al. also noticed this, making mention of the “high degree of locality induced by various externalities, geography chief amongst them”. Then, it is perhaps humbling to know that from us, one world apart stands Asia, but it would still take a couple more worlds on top of that to reach that human connection.


Four Degrees of Separation, Lars Backstrom, Paolo Boldi, Marco Rosa, Johan Ugander, Sebastiano Vigna,, January 2012.

Course textbook – Networks, Crowds, and Markets: Reasoning about a Highly Connected World.


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