Triangle Centrality
@article{Burkhardt2021TriangleC, title={Triangle Centrality}, author={Paul Burkhardt}, journal={ArXiv}, year={2021}, volume={abs/2105.00110} }
Triangle centrality is introduced for finding important vertices in a graph based on the concentration of triangles surrounding each vertex. An important vertex in triangle centrality is at the center of many triangles, and therefore it may be in many triangles or none at all. Given a simple, undirected graph G = (V,E), with n = |V | vertices and m = |E| edges, where N(v) is the neighborhood set of v, N△(v) is the set of neighbors that are in triangles with v, and N + △(v) is the closed set…
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A GraphBLAS Implementation of Triangle Centrality
- Computer Science2021 IEEE High Performance Extreme Computing Conference (HPEC)
- 2021
This paper describes the rapid implementation of triangle centrality using Graph-BLAS, an API specification for describing graph algorithms in the language of linear algebra, and uses Triangle centrality’s algebraic algorithm to implement it using the SuiteSparse GraphBLAS library.
References
SHOWING 1-10 OF 78 REFERENCES
Introduction to parallel algorithms
- Computer ScienceWiley series on parallel and distributed computing
- 1998
The Anatomy of a Large-Scale Hypertextual Web Search Engine
- Computer ScienceComput. Networks
- 1998
Fast sparse matrix multiplication
- Computer ScienceTALG
- 2005
The new algorithm is obtained using a surprisingly straightforward combination of a simple combinatorial idea and existing fast matrix multiplication algorithms, and is faster than the best known matrix multiplication algorithm for dense matrices.
Parallelism in random access machines
- Computer ScienceSTOC
- 1978
A model of computation based on random access machines operating in parallel and sharing a common memory is presented and can accept in polynomial time exactly the sets accepted by nondeterministic exponential time bounded Turing machines.
Bounds and algorithms for graph trusses
- Computer ScienceJ. Graph Algorithms Appl.
- 2020
A simplified and faster algorithm, based on approach discussed in Wang & Cheng (2012), and a theoretical algorithm based on fast matrix multiplication that converts a triangle-generation algorithm of Bjorklund et al. (2014) into a dynamic data structure are presented.
Distribution de la flore alpine dans le bassin des Dranses et dans quelques régions voisines
- Geography
- 1901
A Refined Laser Method and Faster Matrix Multiplication
- Computer ScienceSODA
- 2021
This paper is a refinement of the laser method that improves the resulting value bound for most sufficiently large tensors, and obtains the best bound on $\omega$ to date.
Distributed non-negative matrix factorization with determination of the number of latent features
- Computer ScienceThe Journal of Supercomputing
- 2020
This paper introduces a distributed NMF algorithm coupled with distributed custom clustering followed by a stability analysis on dense data, which it is called DnMFk, to determine the number of latent variables.
GraphBLAST: A High-Performance Linear Algebra-based Graph Framework on the GPU
- Computer ScienceACM Trans. Math. Softw.
- 2022
The design principles described in this paper have been implemented in “GraphBLAST”, the first high-performance linear algebra-based graph framework on NVIDIA GPUs that is open-source, and show that on a single GPU, GraphBLAST has on average at least an order of magnitude speedup over previous GraphBLAS implementations SuiteSparse and GBTL.