Heterogeneous Network Motifs
This work addresses the need for efficient motif analysis in complex heterogeneous networks, which is incremental as it generalizes existing graphlet methods to typed settings.
The authors tackled the problem of counting network motifs in heterogeneous networks by introducing typed graphlets and developing a fast, parallel framework for their enumeration, achieving time complexity matching the best untyped algorithms and demonstrating scalability on large networks.
Many real-world applications give rise to large heterogeneous networks where nodes and edges can be of any arbitrary type (e.g., user, web page, location). Special cases of such heterogeneous graphs include homogeneous graphs, bipartite, k-partite, signed, labeled graphs, among many others. In this work, we generalize the notion of network motifs to heterogeneous networks. In particular, small induced typed subgraphs called typed graphlets (heterogeneous network motifs) are introduced and shown to be the fundamental building blocks of complex heterogeneous networks. Typed graphlets are a powerful generalization of the notion of graphlet (network motif) to heterogeneous networks as they capture both the induced subgraph of interest and the types associated with the nodes in the induced subgraph. To address this problem, we propose a fast, parallel, and space-efficient framework for counting typed graphlets in large networks. We discover the existence of non-trivial combinatorial relationships between lower-order ($k-1$)-node typed graphlets and leverage them for deriving many of the $k$-node typed graphlets in $o(1)$ constant time. Thus, we avoid explicit enumeration of those typed graphlets. Notably, the time complexity matches the best untyped graphlet counting algorithm. The experiments demonstrate the effectiveness of the proposed framework in terms of runtime, space-efficiency, parallel speedup, and scalability as it is able to handle large-scale networks.