He used a customized version of the PageRank algorithm that comes with MATLAB. The paper is pretty dense with other interesting observations. I think one of the novel contributions is experimental evidence that centrality is important to learning distinct sequences of behaviors.

Consider three behaviors: moving right on a linear track, turning around, and moving left. A reinforcement signal could be sugar water. If you place sugar water at the right end of the track the mouse learns the sequence of moving right, drinking, turning around, and moving left to leave. Now, in the hippocampus different ensembles of time and place neurons are correlated with each distinct activity. The inter-ensemble connectivity has to be learned, as the sequence of actions become correlated not just in behavior but in the brain as well. The neurons that most strongly inhabit inter-ensemble connectivity, tend to be those 'stable' and 'important' anchor neurons.

Yes, it has been studied before that some neurons are more important than others. But the critical extension here is to long-term stability and learning on an unprecedented time-scale and quantity of simultaneously recorded neurons. The actual microscope itself, is a significant technological advancement in how it stays robust to long- and short-term motion artifacts and was custom designed and built by the first-author.

There's also the experiment done on dynamics after traumatic damage to the neural circuits encoding a learned behavior (this is one of the specialty of the Lois group). But that starts deviating from the observation I wanted to make relating to the thread.

The conclusion: "Overall, our findings suggest a model where the patterns of activity of individual neurons gradually change over time while the activity of groups of synchronously active neurons ensures the persistence of representations."

Seems fairly innocuous, but I'm almost certain it will be controversial to some parties.