Linear Algebra Approach for Directed Triad Counting and Enumeration

Triangle counting and enumeration are commonly used in real-world applications on directed graphs. However, the performance of triangle counting algorithms is usually bench-marked on undirected graphs. As such, many of these algorithms and formulations are not suitable for identifying the types of d...

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Bibliographic Details
Published in:SC24-W: Workshops of the International Conference for High Performance Computing, Networking, Storage and Analysis pp. 718 - 726
Main Authors: Kerdcharoen, Yuttapichai, Sridhar, Upasana, Sangpetch, Orathai, Low, Tze Meng
Format: Conference Proceeding
Language:English
Published: IEEE 17.11.2024
Subjects:
Conferences
Directed graphs
Fires
graph algorithms
High performance computing
Linear algebra
Object recognition
Optimization
Single instruction multiple data
Systematics
triad census
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Summary:Triangle counting and enumeration are commonly used in real-world applications on directed graphs. However, the performance of triangle counting algorithms is usually bench-marked on undirected graphs. As such, many of these algorithms and formulations are not suitable for identifying the types of directed triangles in directed graphs. In this work, we show how algorithms for counting each type of directed triad (directed triangle) can be formulated using linear algebra. Leveraging the FLAME methodology, we show that provably correct counting and enumeration algorithms for directed triads can be derived from the linear algebraic formulation. These algorithms can be used to count individual triads or together to count all possible triads. We show that despite being designed for individual use, the combined use of these algorithms yields a geometric mean speedup of 92.69x and 2.86x over the implementations in NetworkX and GraphBLAS (SuiteSparse 7.6), respectively, on various workloads from real-world directed graphs.
DOI:10.1109/SCW63240.2024.00100