Measuring Node Contribution to Community Structure With Modularity Vitality

• Published in: IEEE transactions on network science and engineering Vol. 8; no. 1; pp. 707 - 723
• Main Authors: Magelinski, Thomas, Bartulovic, Mihovil, M. Carley, Kathleen
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.01.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Blogs; Clustering algorithms; Communication networks; Community deception; community structure; Digital media; Eigenvalues and eigenfunctions; Modularity; network centrality; network robustness; network vitality; Nodes; Roads; Robustness; Social networking (online); Testing
• ISSN: 2327-4697; 2334-329X
• DOI: 10.1109/TNSE.2020.3049068

Community-aware centrality is an emerging research area in network science concerned with the importance of nodes in relation to community structure. Measures are a function of a network's structure and a given partition. Previous approaches extend classical centrality measures to account for community structure with little connection to community detection theory. In contrast, we propose cluster-quality vitality measures, i.e., modularity vitality, a community-aware measure which is well-grounded in both centrality and community detection theory. Modularity vitality quantifies positive and negative contributions to community structure, which indicate a node's role as a community bridge or hub. We derive a computationally efficient method of calculating modularity vitality for all nodes in <inline-formula><tex-math notation="LaTeX">O(M+NC)</tex-math></inline-formula> time, where <inline-formula><tex-math notation="LaTeX">C</tex-math></inline-formula> is the number of communities. We systematically fragment networks by removing central nodes, and find that modularity vitality consistently outperforms existing community-aware centrality measures. We show measures well-grounded in community theory are over 8 times more effective on a million-node infrastructure network. This result does not generalize to social media communication networks, which exhibit extreme robustness to all community-aware centrality attacks. This robustness suggests that user-based interventions to mitigate misinformation diffusion will be ineffective. Finally, we demonstrate that modularity vitality provides a new approach to community-deception.