Before revision:  Third, we derive the limiting behavior of the maximum modularity Q_max for  infinitely modular networks, showing that it depends strongly  on the size of the network and  the number of module-like subgraphs it contains.
After revision:  Third, we derive the limiting behavior of the maximum modularity Q_max for infinitely modular networks, showing that it depends strongly both on the size of the network and the number of module-like subgraphs it contains.