Lecture 18: Small World Networks

This lecture presented an overview of issues pertaining to small world networks. In particular, small world phenomenon, small world network models, and the formation and occurrences of small world networks were discussed. As an introduction, we were presented with Milgram's experiment which was designed to describe the small world phenomenon. Essentially, although most individuals are not directly connected with one another, each individual can be reached from another through a relatively small number of hops over a network. That is, we are all closer than we think. It was concluded by Milgram that we are connected to any other person on Earth through roughly 6 hops. It is because of this that the term "6 degrees of separation" was coined.

Another criteria for defining small world networks is the natural occurrence of clustering. As example, a short list of social networking sites were presented. Such sites included Facebook, LinkedIn, and VisiblePath. The idea of clustering from a social networking perspective comes from people being drawn towards each other if they are relatively close to each other with respect to the network graph. That is, if people share more common interdependences with each other, they tend to cluster together. Small world networks can thus be simply characterized as having high clustering and low average shortest path.

Next, two social network models were presented: the Watts/Strogatz model and Kleinberg model. These models were made in an attempt to address the characterization of social networks. The Watts/Strogatz model bases their research off of the observation that your friends' friends tend to be your friend as well.

Lastly, a short discussion on the formation of social networks was made. The general idea stems from social theory in that people each have their own set of weighted criteria used in determining friendships or an interest to pursue a friendship. Social networks are very heterogenous in that people are always changing their minds on what it takes for someone to be their friend. Lastly, it is suggested that weak ties are actually very useful in connecting an individual with a larger set of individuals. For example, recent research suggests that those that you don't know very well typically play a largely important role in broadening a social circle,e.g., jobs, new friends, new interests, etc.

In summary, small world networks may evolve from different constraints such as navigation, constraint optimization, and group affiliation.