This way, the network’s modularity becomes the sum over all communities of (4):Similarly, the higher the modularity, the higher the quality of the partition of the network.
In terms of computational complexity, since modularity variation can be calculated in constant time, step 2 requires O(L) calculations.
Although modularity is computationally suited and an accurate way of community detection, two pitfalls should be highlighted: resolution limit and modularity maxima.
Modularity MaximaThe fourth hypothesis presented at the beginning of the article, relies on the assumption that higher modularity implies a better partition of the network.
This plateau explains why a large number of modularity maximization algorithms can quickly detect high modularity partitions — they are not unique.

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