On the formation of structure in growing networks

Based on the formation of triad junctions, the proposed mechanism generates networks that exhibit extended rather than single power law behavior. Triad formation guarantees strong neighborhood clustering and community-level characteristics as the network size grows to infinity. The asymptotic behavior is of interest in the study of directed networks in which (i) the formation of links cannot be described according to the principle of preferential attachment; (ii) the in-degree distribution fits a power law for nodes with a high degree and an exponential form otherwise; (iii) clustering properties emerge at multiple scales and depend on both the number of links that newly added nodes establish and the probability of forming triads; and (iv) groups of nodes form modules that feature less links to the rest of the nodes.Comment: 17 pages, 9 figures, we apply the proposed mechanism to generate network realizations that resemble the degree distribution and clustering properties of an empirical network with no directed cycles (i.e., when the model parameter n=0), updated reference

Power-law weighted networks from local attachments

This letter introduces a mechanism for constructing, through a process of distributed decision-making, substrates for the study of collective dynamics on extended power-law weighted networks with both a desired scaling exponent and a fixed 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 steady state properties of the empirical citation distributions of (i) publications indexed by the Institute for Scientific Information from 1981 to 1997; (ii) patents granted by the U.S. Patent and Trademark Office from 1975 to 1999; and (iii) opinions written by the Supreme Court and the cases they cite from 1754 to 2002.Comment: 18 pages, 3 figures; Proceedings of the IEEE Conference on Decision and Control and the European Control Conference, Orlando, FL, Dec. 2011; Added references; We modified the model in order to take into account extended power-law distributions which better fit to the citations data sets; Added proofs of theorems; Shorten version; Updated plo