Heavy-tailed weighted networks from local attachment strategies

Large networks arise by the gradual addition of nodes attaching to an existing and evolving network component. There are a wide class of attachment strategies which lead to distinct structural features in growing networks. This paper introduces a mechanism for constructing, through a process of distributed decision-making, substrates for the study of collective dynamics on power-law weighted networks with both a desired scaling exponent and a desired clustering coefficient. The analytical results show that the connectivity distribution converges to the scaling behavior often found in social and engineering systems. To illustrate the approach of the proposed framework we generate network substrates that resemble the empirical citation distributions of (i) patents granted by the U.S. Patent and Trademark Office from 1975 to 1999; and (ii) opinions written by the Supreme Court and the cases they cite from 1754 to 2002.