Introduction to Mathematical Sociology by Bonacich Phillip & Lu Philip

Author:Bonacich, Phillip & Lu, Philip [Bonacich, Phillip]
Language: eng
Format: epub
Publisher: Princeton University Press
Published: 2012-04-01T00:00:00+00:00

Clustering in Random Networks

In random networks, the clustering of the network is approximately equal to the density of the network. If on a macro level, the entire random network is dense, then on a micro level, when you examine the local network around a single individual, that network is likely to be dense. Conversely, if the random network is sparse overall, then the local networks around individuals will be sparse as well.

If we use random networks as our model for real-world networks and assume that people could maintain only a finite number of relationships, then in very large populations, the density of such a random network approaches zero. For example, let’s make the reasonable assumption that, on average, someone maintains 30 friendships. Since each friendship tie consists of two people, then in this network, each person will contribute 15 to the number of edges (m = 15n). Thus the formula for the density of this network is,

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