Heterogeneous Network Motif Coding, Counting, and Profiling

Network motifs, as a fundamental higher-order structure in large-scale networks, have received significant attention over recent years. Particularly in heterogeneous networks, motifs offer a higher capacity to uncover diverse information compared to homogeneous networks. However, the structural complexity and heterogeneity pose challenges in coding, counting, and profiling heterogeneous motifs. This work addresses these challenges by first introducing a novel heterogeneous motif coding method, adaptable to homogeneous motifs as well. Building upon this coding framework, we then propose GIFT, a heterogeneous network motif counting algorithm. GIFT effectively leverages combined structures of heterogeneous motifs through three key procedures: neighborhood searching, motif combination, and redundant motif filtering. We apply GIFT to count three-order and four-order motifs across eight distinct heterogeneous networks. Subsequently, we profile these detected motifs using four classical motif-based indicators. Experimental results demonstrate that by appropriately selecting motifs tailored to specific networks, heterogeneous motifs emerge as significant features in characterizing the underlying network structure.