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 O(M + NC) time, where C 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. Modularity vitality is over 8 times more effective than the next-best method 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.

中文翻译：

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用模块化活力衡量节点对社区结构的贡献

社区感知中心性是网络科学中一个新兴的研究领域，关注节点对社区结构的重要性。度量是网络结构和给定分区的函数。以前的方法扩展了经典的中心性度量以解释与社区检测理论几乎没有联系的社区结构。相比之下，我们提出了集群质量的活力措施，即模块化活力，这是一种社区感知措施，在中心性和社区检测理论中都有很好的基础。模块化活力量化了对社区结构的积极和消极贡献，这表明节点作为社区桥梁或枢纽的作用。我们推导出一种计算效率高的方法，可以在 O(M + NC) 时间内计算所有节点的模块化生命力，其中 C 是社区的数量。我们通过移除中心节点来系统地分割网络，并发现模块化生命力始终优于现有的社区感知中心性度量。模块化生命力比百万节点基础设施网络上的次优方法有效 8 倍以上。这个结果不能推广到社交媒体通信网络，社交媒体通信网络对所有社区感知中心性攻击都表现出极端的鲁棒性。这种稳健性表明，基于用户的干预措施来减轻错误信息的传播将是无效的。最后，我们证明了模块化生命力为社区欺骗提供了一种新方法。模块化生命力比百万节点基础设施网络上的次优方法有效 8 倍以上。这个结果不能推广到社交媒体通信网络，社交媒体通信网络对所有社区感知中心性攻击都表现出极端的鲁棒性。这种稳健性表明，基于用户的干预措施来减轻错误信息的传播将是无效的。最后，我们证明了模块化生命力为社区欺骗提供了一种新方法。模块化生命力比百万节点基础设施网络上的次优方法有效 8 倍以上。这个结果不能推广到社交媒体通信网络，社交媒体通信网络对所有社区感知中心性攻击都表现出极端的鲁棒性。这种稳健性表明，基于用户的干预措施来减轻错误信息的传播将是无效的。最后，我们证明了模块化生命力为社区欺骗提供了一种新方法。