Bounds and algorithms for $k$-truss
arXiv: Combinatorics(2019)
摘要
A $k$-truss is a relaxation of a $k$-clique developed by Cohen (2005), specifically a connected graph where every edge is incident to at least $k$ triangles. This has proved to be a useful tool in identifying cohesive subnetworks in a variety of real-world graphs. Despite its simplicity and its utility, the combinatorial and algorithmic aspects of trusses have not been thoroughly explored. We provide nearly-tight bounds on the edge counts of $k$-trusses. We also give two improved algorithms for finding trusses in large-scale graphs. First, we present a simplified and faster algorithm, based on approach discussed in Wang & Cheng (2012). Second, we present a theoretical algorithm based on fast matrix multiplication; this extends an algorithm of Bjorklund et al. (2014) for generating triangles from a static graph to a dynamic data-structure.
更多查看译文
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要