Block-corrected Modularity for Community Detection

Abstract

Unknown node attributes in complex networks may introduce community structures that are important to distinguish from those driven by known attributes. We propose a block-corrected modularity that discounts given block structures present in the network to reveal communities masked by them. We show analytically how the proposed modularity finds the community structure driven by an unknown attribute in a simple network model. Further, we observe that the block-corrected modularity finds the underlying community structure on a number of simple synthetic network models while methods using different null models fail. We develop an efficient spectral method as well as two Louvain-inspired fine-tuning algorithms to maximize the proposed modularity and demonstrate their performance on several synthetic network models. Finally, we assess our methodology on various real-world citation networks built using the OpenAlex data by correcting for the temporal citation patterns.

22 pages, 11 figures

References in corpus (29)

• Fast unfolding of communities in large networks
• Community structure in social and biological networks
• Modularity and community structure in networks
• Finding community structure in very large networks
• Natural Scales in Geographical Patterns
• Finding community structure in networks using the eigenvectors of matrices
• Stochastic blockmodels and community structure in networks
• Community structure in directed networks
• The performance of modularity maximization in practical contexts
• Mathematical Formulation of Multi-Layer Networks
• Modularity from Fluctuations in Random Graphs and Complex Networks
• Modularity and community detection in bipartite networks
• Social Structure of Facebook Networks
• The ground truth about metadata and community detection in networks
• Community detection in networks with positive and negative links
• Structure and inference in annotated networks
• Uncovering space-independent communities in spatial networks
• Comparing Community Structure to Characteristics in Online Collegiate Social Networks
• Community detection in networks: Structural communities versus ground truth
• Attention decay in science
• Motif-based communities in complex networks
• When are networks truly modular?
• Random graph models for directed acyclic networks
• Spectral tripartitioning of networks
• Descriptive vs. inferential community detection in networks: pitfalls, myths, and half-truths
• Network structure, metadata and the prediction of missing nodes and annotations
• Community detection in directed acyclic graphs
• Separating Polarization from Noise: Comparison and Normalization of Structural Polarization Measures
• Quantifying metadata relevance to network block structure using description length