Watts' model of cascading network failure

I have written in the past about how social and economic networks are a necessary ingredient for a proper understanding of economic patterns. The rise of social network platforms like Facebook and Twitter has allowed a thorough analysis of empirical regularities seen in networks in the social domain. Stephen Wolfram has a great blog about the regularities observed in Facebook data scraped using WolframAlpha.

One of the more interesting networks models is Duncan Watts' model of cascading network failure. Simply, each node in the network has a specific tolerance to failure, and it the share of adjoining nodes that have failed exceeds this tolerance, that node will also fail. For example, a node could have a tolerance of 0.5, so if more than half of its neighbours have failed, it will also fail, leading to a cascade of failures of its other neighbours.

This simple model is quite versatile. It suggests underlying mechanisms behind how fashion fads arise, or why investors tend to go with the herd, or why some industries produce superstars even though no one can objectively tell the difference in the quality of their skills. 

The methodological individualism so fondly embraced by the economics crowd has at its core the concept of utility, but stops short of answering the far more important question – where does our utility function come from if not our environment and our interactions with others? A model of networks can help explain the source of utility and begin to give a picture of how unique cultures and customs arise. 

In any case, I have generated an animated version of the model that simulates over a random network, with 5 random nodes ‘shocked’ to initiate the model. The histogram shows how many of the 20 different shocks have led to cascades of failure of a particular number of nodes. 

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