Modularity optimization can miss “intuitively modular structures”.

Both subfigures show the same network, comprised of a small subnet of 5 nodes with a single link to a large subnet of 1,000 nodes. A: The network as constructed; small subnet nodes are blue and large subnet nodes are red. For this partition, Q ≈ .005, , . B: The result of a modularity-optimizing community detection algorithm, with the two “communities” in yellow and green. Note that the algorithm completely misses the constructed partition of small and large subnets. For this partition, Q ≈ .156.