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Finding Cliques in Social Networks: A New Distribution-Free Model
SIAM Journal on Computing ( IF 1.6 ) Pub Date : 2020-04-27 , DOI: 10.1137/18m1210459
Jacob Fox , Tim Roughgarden , C. Seshadhri , Fan Wei , Nicole Wein

SIAM Journal on Computing, Volume 49, Issue 2, Page 448-464, January 2020.
We propose a new distribution-free model of social networks. Our definitions are motivated by one of the most universal signatures of social networks, triadic closure---the property that pairs of vertices with common neighbors tend to be adjacent. Our most basic definition is that of a $c$-closed graph, where for every pair of vertices $u,v$ with at least $c$ common neighbors, $u$ and $v$ are adjacent. We study the classic problem of enumerating all maximal cliques, an important task in social network analysis. We prove that this problem is fixed-parameter tractable with respect to $c$ on $c$-closed graphs. Our results carry over to weakly $c$-closed graphs, which only require a vertex deletion ordering that avoids pairs of nonadjacent vertices with $c$ common neighbors. Numerical experiments show that well-studied social networks with thousands of vertices tend to be weakly $c$-closed for modest values of $c$.


中文翻译:

在社交网络中寻找团体:一种新的免费发行模型

SIAM计算杂志,第49卷,第2期,第448-464页,2020年1月。
我们提出了一种新的无分配的社交网络模型。我们的定义是受社交网络最普遍的特征之一,即三重闭锁(triadicclosure)的启发,三叉闭锁是指具有共同邻居的一对顶点趋于相邻的属性。我们最基本的定义是一个封闭的$ c $图,其中对于每对具有至少$ c $个公共邻居的顶点$ u,v $,它们彼此相邻。我们研究了枚举所有最大派系的经典问题,这是社交网络分析中的一项重要任务。我们证明,相对于$ c $闭合图中的$ c $,此问题是固定参数可处理的。我们的结果延续到了弱的$ c $封闭图,该图仅需要一个顶点删除顺序即可避免成对的非相邻顶点与$ c $的公共邻居。
更新日期:2020-04-27
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