Broad Institute of MIT and Harvard, Cambridge, MA 02142.
HHMI, Yale University School of Medicine, New Haven, CT 06510.
Proc Natl Acad Sci U S A. 2022 Aug 9;119(32):e2204967119. doi: 10.1073/pnas.2204967119. Epub 2022 Aug 1.
Networks are fundamental for our understanding of complex systems. The study of networks has uncovered common principles that underlie the behavior of vastly different fields of study, including physics, biology, sociology, and engineering. One of these common principles is the existence of network motifs-small recurrent patterns that can provide certain features that are important for the specific network. However, it remains unclear how network motifs are joined in real networks to make larger circuits and what properties emerge from interactions between network motifs. Here, we develop a framework to explore the mesoscale-level behavior of complex networks. Considering network motifs as hypernodes, we define the rules for their interaction at the network's next level of organization. We develop a method to infer the favorable arrangements of interactions between network motifs into hypermotifs from real evolved and designed network data. We mathematically explore the emergent properties of these higher-order circuits and their relations to the properties of the individual minimal circuit components they combine. We apply this framework to biological, neuronal, social, linguistic, and electronic networks and find that network motifs are not randomly distributed in real networks but are combined in a way that both maintains autonomy and generates emergent properties. This framework provides a basis for exploring the mesoscale structure and behavior of complex systems where it can be used to reveal intermediate patterns in complex networks and to identify specific nodes and links in the network that are the key drivers of the network's emergent properties.
网络对于我们理解复杂系统至关重要。对网络的研究揭示了普遍存在的原则，这些原则是物理学、生物学、社会学和工程学等截然不同的研究领域行为的基础。这些普遍原则之一是网络基元的存在——小的重复模式，这些模式可以提供特定网络的某些重要特征。然而，目前尚不清楚网络基元如何在真实网络中连接形成更大的回路，以及网络基元之间的相互作用会产生什么特性。在这里，我们开发了一个框架来探索复杂网络的中尺度行为。我们将网络基元视为超节点，并定义了它们在网络下一层次组织中的相互作用规则。我们开发了一种从真实进化和设计的网络数据中推断网络基元之间有利相互作用安排的方法，以形成超基元。我们从数学上探讨了这些高阶回路的涌现特性以及它们与所组合的单个最小回路组件的特性之间的关系。我们将这个框架应用于生物、神经元、社会、语言和电子网络，发现网络基元在真实网络中并非随机分布，而是以一种既能保持自主性又能产生涌现特性的方式组合在一起。这个框架为探索复杂系统的中尺度结构和行为提供了基础，它可以用来揭示复杂网络中的中间模式，并确定网络中对网络涌现特性起关键驱动作用的特定节点和链路。
