模块化网络源于多约束优化
Modular networks emerge from multiconstraint optimization
摘要：
模块化结构在复杂网络中普遍存在。我们注意到，大多数这样的系统受到多种结构和功能约束，例如，最小化平均路径长度和链路总数，同时最大化对节点活动中的扰动的鲁棒性。我们证明了满足这三个约束的最优网络的特征在于存在多个彼此稀疏连接的子网络（模块）。此外，这些模块有不同的枢纽，导致整体异构度分布。
英文摘要：
Modular structure is ubiquitous among complex networks. We note that most such systems are subject to multiple structural and functional constraints, e.g., minimizing the average path length and the total number of links, while maximizing robustness against perturbations in node activity. We show that the optimal networks satisfying these three constraints are characterized by the existence of multiple subnetworks (modules) sparsely connected to each other. In addition, these modules have distinct hubs, resulting in an overall heterogeneous degree distribution.
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