Community structure is one of the most relevant features encountered in numerous real-world applications of networked systems. Despite the tremendous effort of a large interdisciplinary community of scientists working on this subject over the past few decades to characterize, model, and analyze communities, more investigations are needed in order to better understand the impact of community structure and its dynamics on networked systems. Here, we first focus on generative models of communities in complex networks and their role in developing strong foundation for community detection algorithms. We discuss modularity and the use of modularity maximization as the basis for community detection. Then, we follow with an overview of the Stochastic Block Model and its different variants as well as inference of community structures from such models. Next, we focus on time evolving networks, where existing nodes and links can disappear, and in parallel new nodes and links may be introduced. The extraction of communities under such circumstances poses an interesting and non-trivial problem that has gained considerable interest over the last decade. We briefly discuss considerable advances made in this field recently. Finally, we focus on immunization strategies essential for targeting the influential spreaders of epidemics in modular networks. Their main goal is to select and immunize a small proportion of individuals from the whole network to control the diffusion process. Various strategies have emerged over the years suggesting different ways to immunize nodes in networks with overlapping and non-overlapping community structure. We first discuss stochastic strategies that require little or no information about the network topology at the expense of their performance. Then, we introduce deterministic strategies that have proven to be very efficient in controlling the epidemic outbreaks, but require complete knowledge of the network.

中文翻译：

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关于复杂网络中的社区结构：挑战与机遇

社区结构是在网络系统的许多实际应用中遇到的最相关的功能之一。尽管在过去的几十年中，跨学科的大型科学家社区为表征，建模和分析社区付出了巨大的努力，但仍需要进行更多调查，以更好地了解社区结构及其动态性对网络系统的影响。在这里，我们首先关注复杂网络中社区的生成模型，以及它们在为社区检测算法奠定坚实基础方面的作用。我们讨论模块化和模块化最大化的使用作为社区检测的基础。然后，我们将概述随机块模型及其不同的变体，并从这些模型中推断出群落结构。下一个，我们关注的是时间演变的网络，其中现有的节点和链接可能会消失，与此同时，可能会引入新的节点和链接。在这种情况下，社区的抽取带来了一个有趣而又不平凡的问题，在过去十年中引起了人们的极大兴趣。我们简要地讨论了最近在该领域取得的重大进展。最后，我们重点关注针对模块化网络中有影响力的流行病传播者必不可少的免疫策略。他们的主要目标是从整个网络中选择并免疫一小部分个体，以控制扩散过程。这些年来出现了各种策略，这些策略提出了以不同和不重叠的社区结构对网络中的节点进行免疫的不同方法。我们首先讨论随机策略，这些策略只需要很少或根本不需要有关网络拓扑的信息，而以它们的性能为代价。然后，我们介绍确定性策略，这些策略已被证明在控制流行病爆发方面非常有效，但需要对网络有完整的了解。