# Motif Counting in Complex Networks: A Comprehensive Survey

arXiv: https://arxiv.org/abs/2503.19573 · HTML: https://mlsanity.com/paper/2503.19573/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2025.

## Built on by (most cited first, 1 of 1)

- [Measuring Structure in Graph Benchmark Datasets Using Graph Invariants](https://mlsanity.com/paper/2605.06462/) (2026)

## Abstract (arXiv)

Motif counting plays a crucial role in understanding the structural properties of networks. By computing motif frequencies, researchers can draw key insights into the structural properties of the underlying network. As networks become increasingly complex, different graph models have been proposed, giving rise to diverse motif patterns. These variations introduce unique computational challenges that require specialized algorithms tailored to specific motifs within different graph structures. This survey provides a comprehensive and structured overview of motif counting techniques across general graphs, heterogeneous graphs, and hypergraphs. We categorize existing algorithms according to their underlying computational strategies, emphasizing key similarities and distinctions. In addition to reviewing current methodologies, we examine their strengths, limitations, and computational trade-offs. Furthermore, we explore future directions in motif counting, including scalable implementations to improve efficiency in large-scale networks, algorithmic adaptations for dynamic, temporal, and attributed graphs, and deeper integration with large language models (LLMs) and graph-based retrieval-augmented generation (GraphRAG). By offering a detailed analysis of these approaches, this survey aims to support researchers and practitioners in advancing motif counting for increasingly complex network data.