Networks exhibit rich and diverse higher-order organizational structures. Network motifs, which are recurring significant patterns of inter-connections, are recognized as fundamental units to study the higher-order organizations of networks. However, the principle of selecting representative network motifs for local motif based clustering remains largely unexplored. We present a scalable algorithm called FSM for network motif discovery. FSM is advantageous in two-fold. First, it accelerates the motif discovery process by effectively reducing the number of times for subgraph isomorphism labeling. Second, FSM adopts multiple heuristic optimizations for subgraph enumeration and classification to further improve its performance. Experimental results on biological networks show that, comparing with the existing network motif discovery algorithm, FSM is more efficient on computational efficiency and memory usage. Furthermore, with the large, frequent, and sparse network motifs discovered by FSM, the higher-order organizational structures of biological networks were successfully revealed, indicating that FSM is suitable to select network representative network motifs for exploring high-order network organizations.

中文翻译：

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FSM：用于探索高阶网络组织的快速且可扩展的网络 Motif 发现

网络表现出丰富多样的高阶组织结构。网络模体是反复出现的重要互连模式，被认为是研究网络高阶组织的基本单位。然而，为基于局部模体的聚类选择代表性网络模体的原则在很大程度上仍未被探索。我们提出了一种称为 FSM 的可扩展算法，用于网络基序发现。FSM 有两方面的优势。首先，它通过有效减少子图同构标记的次数来加速主题发现过程。其次，FSM 对子图枚举和分类采用多重启发式优化，以进一步提高其性能。在生物网络上的实验结果表明，与现有的网络基序发现算法相比，FSM 在计算效率和内存使用方面更高效。此外，利用 FSM 发现的大、频繁和稀疏的网络模体，成功揭示了生物网络的高阶组织结构，表明 FSM 适合选择网络代表网络模体来探索高阶网络组织。