Tools for higher-order network analysis
This work provides incremental tools for researchers in network science to analyze higher-order connectivity patterns across various domains.
The paper tackled the problem of analyzing complex networks by developing three tools for higher-order network analysis, including node clustering based on motifs, a generalized clustering coefficient, and motif definitions for temporal networks, and applied these tools to diverse datasets from fields like biology and economics.
Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order connectivity patterns captured by small subgraphs, also called network motifs, describe the fundamental structures that control and mediate the behavior of many complex systems. We develop three tools for network analysis that use higher-order connectivity patterns to gain new insights into network datasets: (1) a framework to cluster nodes into modules based on joint participation in network motifs; (2) a generalization of the clustering coefficient measurement to investigate higher-order closure patterns; and (3) a definition of network motifs for temporal networks and fast algorithms for counting them. Using these tools, we analyze data from biology, ecology, economics, neuroscience, online social networks, scientific collaborations, telecommunications, transportation, and the World Wide Web.