NI-ORCA: A Parallel Algorithm for Counting the Orbits of Non-Induced Graphlets up to K4

2026-06-28

AI Summary

Existing methods struggle to efficiently and precisely count non-induced graphlet orbits in parallel, limiting their practical applicability. This work proposes NI-ORCA, the first algorithm to enable exact parallel counting of non-induced graphlet orbits up to size K4. By reformulating the underlying system of linear equations, NI-ORCA decomposes the computation into three stages—triangle counting, 4-clique enumeration, and orbit resolution—and employs stage-specific data structures, dynamic task scheduling, fine-grained task partitioning, and affinity-aware strategies to optimize load balancing and minimize resource contention under a thread- and vertex-local memory model. Experimental results demonstrate that NI-ORCA achieves up to a 30× speedup over the current best serial algorithm on both real-world and synthetic graphs, substantially improving scalability and computational efficiency.

Abstract

Counting the orbits of graphlets in a network is a vital tool for understanding the structural roles of vertices in various graph analytics tasks. While existing algorithms efficiently compute orbits of induced graphlets, many real-world applications require non-induced orbit counts. However, no current method offers exact, scalable, and parallel support for non-induced orbit counting. This paper presents NI-ORCA, a parallel algorithm to efficiently compute the orbits of non-induced graphlets up to size four (4-clique). NI-ORCA extends the ORCA framework for non-induced orbit counting by reformulating a system of linear equations. The algorithm consists of three stages: triangle counting, 4-clique enumeration, and orbit solving. We design and implement stage-specific parallelisation strategies using thread and vertex-local memory models and data structures, minimising contention and balancing workload. We further analyse the impact of scheduling policies, chunk sizes, and affinity strategies on performance. Experimental analysis on eight real-world datasets and a series of synthetic Erddos-Renyi graphs demonstrates that a mixed mode combining stage-specific data structure, with dynamic scheduling with small chunk sizes, delivers consistent speedup and effective load balancing. Our results show that NI-ORCA significantly outperforms state-of-the-art sequential algorithms, achieving up to 30x speedups.

Problem

• non-induced graphlets
• orbit counting
• parallel algorithm
• graph analytics
• scalable computation

Innovation

• non-induced graphlets
• orbit counting
• parallel algorithm
• graph analytics
• load balancing