  We introduce the concepts of closed sets and closure operators as
mathematical tools for the study of social networks. Dynamic networks are
represented by transformations. It is shown that under continuous
change/transformation, all networks tend to "break down" and become less
complex. It is a kind of entropy. The product of this theoretical decomposition
is an abundance of triadically closed clusters which sociologists have observed
in practice. This gives credence to the relevance of this kind of mathematical
analysis in the sociological context.
