Testing theories of preferential attachment in random networks of citations

In this article we examine 2 classic stochastic models of the accumulation of citations introduced by H.A. Simon and Derek John de Solla Price. These models each have 2 distinct aspects: growth, which is the introduction of new articles, and preferential attachment, which describes how established articles accumulate new citations. The attachment rules are the subtle portion of these models that supply the interesting explanatory power. Previous treatments included both aspects. Here we separate preferential attachment from the growth aspect of the model. This separation allows us to examine the results of the preferential attachment rules without confounding these with growth in the number of articles available to receive citations. We introduce the method using Markov chains. We show how to overcome the mathematical and computational complexity to obtain results. A comparison of Simon's and Price's rules are computed in 3 Journal Citation Reports subject categories using articles published in the 1960s and allowed to accumulate citations to 1980. This comparison cannot be made through analysis of power laws.