  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.
