The paper defines energy modularity, a self-sufficiency-based community detection objective, and a scalable Louvain algorithm that optimizes it with flexibility activation.
Partitioning and modularity of graphs with arbitrary degree distribution
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abstract
We solve the graph bi-partitioning problem in dense graphs with arbitrary degree distribution using the replica method. We find the cut-size to scale universally with <k^1/2>. In contrast, earlier results studying the problem in graphs with a Poissonian degree distribution had found a scaling with <k>^1/2 [Fu and Anderson, J. Phys. A: Math. Gen. 19, 1986]. The new results also generalize to the problem of q-partitioning. They can be used to find the expected modularity Q [Newman and Grivan, Phys. Rev. E, 69, 2004] of random graphs and allow for the assessment of statistical significance of the output of community detection algorithms.
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Community Detection in Energy Networks based on Energy Self-Sufficiency and Dynamic Flexibility Activation
The paper defines energy modularity, a self-sufficiency-based community detection objective, and a scalable Louvain algorithm that optimizes it with flexibility activation.