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Every network scientist knows that preferential attachment combines withgrowth to produce networks with power-law in-degree distributions. How, then,is it possible for the network of American Physical Society journal collectioncitations to enjoy a log-normal citation distribution when it was found to havegrown in accordance with preferential attachment? This anomalous result, whichwe exalt as the preferential attachment paradox, has remained unexplained sincethe physicist Sidney Redner first made light of it over a decade ago. Here wepropose a resolution. The chief source of the mischief, we contend, lies inRedner having relied on a measurement procedure bereft of the accuracy requiredto distinguish preferential attachment from another form of attachment that isconsistent with a log-normal in-degree distribution. There was a high-accuracymeasurement procedure in use at the time, but it would have have been difficultto use it to shed light on the paradox, due to the presence of a systematicerror inducing design flaw. In recent years the design flaw had been recognisedand corrected. We show that the bringing of the newly corrected measurementprocedure to bear on the data leads to a resolution of the paradox.

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