A High-Performance Evolutionary Multiobjective Community Detection Algorithm

TL;DR

HP-MOCD tackles large-scale, multi-objective community detection by framing partitioning as a two-objective optimization problem that balances intra-community density and balanced community sizes. Built on NSGA-II with topology-aware crossover and mutation, and implemented in a parallel, open-source Rust/Python stack, it achieves $O(GN_p|V|)$ total complexity on sparse graphs. The method produces a Pareto front of high-quality partitions, enabling decision-makers to trade off structural cohesion against size balance, and demonstrates strong scalability to graphs with over $10^6$ nodes while maintaining competitive accuracy. Across synthetic and real-world benchmarks, HP-MOCD outperforms other MOEAs in runtime and robustness, and remains competitive with single-objective baselines, offering a practical, flexible tool for large-scale network analysis.

Abstract

Community detection in complex networks is fundamental across social, biological, and technological domains. While traditional single-objective methods like Louvain and Leiden are computationally efficient, they suffer from resolution bias and structural degeneracy. Multi-objective evolutionary algorithms (MOEAs) address these limitations by simultaneously optimizing conflicting structural criteria, however, their high computational costs have historically limited their application to small networks. We present HP-MOCD, a High-Performance Evolutionary Multiobjective Community Detection Algorithm built on Non-dominated Sorting Genetic Algorithm II (NSGA-II), which overcomes these barriers through topology-aware genetic operators, full parallelization, and bit-level optimizations, achieving theoretical O(GN_p|V|) complexity. We conduct experiments on both synthetic and real-world networks. Results demonstrate strong scalability, with HP-MOCD processing networks of over 1,000,000 nodes while maintaining high quality across varying noise levels. It outperforms other MOEAs by more than 531 times in runtime on synthetic datasets, achieving runtimes as low as 57 seconds for graphs with 40,000 nodes on moderately powered hardware. Across 14 real-world networks, HP-MOCD was the only MOEA capable of processing the six largest datasets within a reasonable time, with results competitive with single-objective approaches. Unlike single-solution methods, HP-MOCD produces a Pareto Front, enabling individual-specific trade-offs and providing decision-makers with a spectrum of high-quality community structures. It introduces the first open-source Python MOEA library compatible with networkx and igraph for large-scale community detection.

Figures (10)

• Figure 1: A conceptual illustration of community structure. The network is partitioned into two distinct communities (blue and green). The solid gray lines represent dense intra-community edges, which create cohesive groups. The single dashed red line represents a sparse inter-community edge (or bridge), highlighting the weak connectivity between the groups. The goal of community detection is to identify such partitions.
• Figure 2: Flowchart of the HP-MOCD algorithm. Green-highlighted boxes indicate parallel operations that enhance computational efficiency. The algorithm iteratively evolves populations through selection, crossover, mutation, and environmental selection until convergence.
• Figure 3: (a) A simple network with some nodes that shows aspects of a community. (b) The same network, but with distinct communities. Nodes within each community (blue, green, and red) are more densely connected internally, with sparser connections between communities.
• Figure 4: Analysis of the scalarization-based selection method. The red dot highlights the solution with the highest value of $Q(C)$.
• Figure 5: Performance results across varying $maxgen$ values with $\mu = 0.1$. Refer to \ref{['sec:paramters-setup']} for details on the experimental setup.