The asymptotic distribution of modularity in weighted signed networks.

@article{Ma2021TheAD,
  title={The asymptotic distribution of modularity in weighted signed networks.},
  author={Rong Ma and Ian Barnett},
  journal={Biometrika},
  year={2021},
  volume={108 1},
  pages={
          1-16
        }
}
Modularity is a popular metric for quantifying the degree of community structure within a network. The distribution of the largest eigenvalue of a network's edge weight or adjacency matrix is well studied and is frequently used as a substitute for modularity when performing statistical inference. However, we show that the largest eigenvalue and modularity are asymptotically uncorrelated, which suggests the need for inference directly on modularity itself when the network size is large. To this… 

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