Kevin E. Bassler

Tania Ghosh, Kevin E. Bassler

Many bipartite networks exhibit hierarchical community structure, but existing community detection methods are not well-suited for detecting hierarchy. They also do not effectively handle weighted bipartite networks. In this work, we introduce a novel modularity-based objective function, called the generalized bipartite modularity density, Qbg, specifically designed for hierarchical community detection in bipartite systems. The framework incorporates a tunable resolution parameter that enables systematic exploration of community structure across multiple scales. It leverages resolution-limit behavior in bipartite networks as a tool to uncover hierarchical organization without projecting the network or altering its intrinsic bipartite topology. We evaluate the method using a hierarchical synthetic bipartite benchmark and apply it to two empirical networks. In all cases, Qbg recovers established mesoscale structure while revealing additional hierarchical and fine-scale organization beyond that detected by conventional bipartite approaches. These results establish Qbg as a flexible, interpretable, and resolution-aware framework for hierarchical community detection in bipartite networks.

Jiahao Guo, Pramesh Singh, Kevin E. Bassler

We introduce an ensemble learning scheme for community detection in complex networks. The scheme uses a Machine Learning algorithmic paradigm we call Extremal Ensemble Learning. It uses iterative extremal updating of an ensemble of network partitions, which can be found by a conventional base algorithm, to find a node partition that maximizes modularity. At each iteration, core groups of nodes that are in the same community in every ensemble partition are identified and used to form a reduced network. Partitions of the reduced network are then found and used to update the ensemble. The smaller size of the reduced network makes the scheme efficient. We use the scheme to analyze the community structure in a set of commonly studied benchmark networks and find that it outperforms all other known methods for finding the partition with maximum modularity.