Fig. 5: Schematic of cluster partition method in the network model by maximizing modularity with the Louvain algorithm. | Nature Communications

Fig. 5: Schematic of cluster partition method in the network model by maximizing modularity with the Louvain algorithm.

From: Modularity-based mathematical modeling of ligand inter-nanocluster connectivity for unraveling reversible stem cell regulation

Fig. 5

Modularity helps to quantify the interconnectivity of clusters within a network. Factors used in such quantification in the modularity formula include the total number of edges (m), the presence of an edge between the two nodes (Aij), the number of edges from each node (ki or kj), and the cluster coincidence of node pair [\(\delta\)(Ci, Cj)]. The modularity is maximized in the optimal cluster partition where the number of intra-cluster (within the cluster) edges is maximized while the number of inter-cluster (between the clusters) edges is minimized. The optimized cluster partition of a given network can be found using the Louvain algorithm in Python, where this formula is included.

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