A Preferential Attachment Paradox: How Preferential Attachment Combines with Growth to Produce Networks with Log-normal In-degree Distributions

Abstract

Every network scientist knows that preferential attachment combines with growth to produce networks with power-law in-degree distributions. How, then, is it possible for the network of American Physical Society journal collection citations to enjoy a log-normal citation distribution when it was found to have grown in accordance with preferential attachment? This anomalous result, which we exalt as the preferential attachment paradox, has remained unexplained since the physicist Sidney Redner first made light of it over a decade ago. Here we propose a resolution. The chief source of the mischief, we contend, lies in Redner having relied on a measurement procedure bereft of the accuracy required to distinguish preferential attachment from another form of attachment that is consistent with a log-normal in-degree distribution. There was a high-accuracy measurement procedure in use at the time, but it would have have been difficult to use it to shed light on the paradox, due to the presence of a systematic error inducing design flaw. In recent years the design flaw had been recognised and corrected. We show that the bringing of the newly corrected measurement procedure to bear on the data leads to a resolution of the paradox.

13 pages, 4 figures, 2 table, 1 supplementary notes file; fixed broken figure and table references

References in corpus (8)

• Power-law distributions in empirical data
• Modern temporal network theory: A colloquium
• Fitting heavy tailed distributions: the poweRlaw package
• Generalization of Blonder-Tinkham-Klapwijk theory to particle-hole mixing boundary conditions: π-shift and conductance dips
• Growing complex network of citations of scientific papers -- measurements and modeling
• Stochastic dynamical model of a growing network based on self-exciting point process
• Preferential attachment during the evolution of a potential energy landscape
• Preferential Attachment in Online Networks: Measurement and Explanations

Cited by in corpus (8)

• Unraveling the dynamics of growth, aging and inflation for citations to scientific articles from specific research fields
• New Phenomena in Large-Scale Internet Traffic
• Identifying time dependence in network growth
• PAFit: an R Package for the Non-Parametric Estimation of Preferential Attachment and Node Fitness in Temporal Complex Networks
• Scientometric engineering: Exploring citation dynamics via arXiv eprints
• Onion under Microscope: An in-depth analysis of the Tor network
• Hybrid Power-Law Models of Network Traffic
• Degree distributions in networks: beyond the power law