#small-world

The McKechnie Institute: Saturday 30th June - Saturday 22nd September 2018

Pillar Gallery

For the summer months, the popular Small World exhibition returns with collections in miniature of cars, railways and dolls’ houses. This is a great display for all ages to visit and enjoy.

This week’s topic was on Synchronicity and Small World Dynamics. As an intro, to better understand synchronicity, we discussed our previous notions of emergence. After some looks at disappointing Wikipedia definitions, we agreed that these topics described a disconnect between behavior at the different levels of a system.

On the subject of small-world dynamics, we looked at Strogatz method of rewiring random networks: connecting each node to its closest k neighbors, and then with probability p, reconnecting each node in a clockwise fashion to a randomly chosen node in the graph. We then examined the local clustering coefficients as p increased, trying to intuit at every step. Strogatz furthered that this method worked well to model disease transmission, and collaboration between artists on imdb.

Later on we discussed random graphs, particularly Erdős graphs where edges are created with probability p. At around p > 1/N, for N nodes in a graph, it is almost guaranteed to have unconnected parts with one large connected component. These graphs have a rigid degree distribution that does not model real-world networks well. To better understand those real networks, we then looked at a method by Barábasi to describe such ‘scale-free networks.’ This method starts with a strongly connected component, such as the Erdős graph, and adds new nodes that are connected a pre-existing node i with probability proportional to the degree of i. It can be shown that the resulting degree distribution is a negative exponential. The intuiting of the method is that new friends are more likely to connect with the most popular nodes.