期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2022
卷号：119
期号：32
DOI：10.1073/pnas.2204967119
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Significance
Complex systems with multiple components that influence each other, from societies to interacting genes, can be studied using a network description. The nodes in a network are the atoms. Just as atoms combine into molecules that have new properties, nodes combine into network motifs—building-block patterns that frequently recur in the network and have certain dynamic properties. But how are these building blocks combined in networks and what properties emerge when they interact with each other? Here, we define hypermotifs—arrangements of network motif assemblies. We identify enriched hypermotifs in real networks and find that each type of network is enriched in specific hypermotifs that show new dynamic properties. This framework defines the next level of organization in complex networks.
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.
